Solution 1:

I am suffering at prolem 1 as well but there is the plugin called 'Slide for Keyboard' available and this solves the problem partially. If activated, this plugin causes the keyboard to appear when doing an edge slide from the bottom of the screen. Here is the link: https://extensions.gnome.org/extension/993/slide-for-keyboard/

You may want another keyboard layout for vertical view. You can define your own keyboard layout using XML for that. Take a look at the directory /usr/share/caribou/layouts

Use the same XML Syntax as in some already existing layouts. I use a German layout and my config for vertical keyboard looks like this:

<?xml version="1.0"?>
<layout xmlns:xi="http://www.w3.org/2001/XInclude">
  <level mode="default" name="level1" xml:base="common/qwerty.xml">
    <row>
      <key name="Escape"/>
      <key name="q"/>
      <key name="w"/>
      <key name="e">
        <key name="e"/>
        <key name="egrave"/>
        <key name="eacute"/>
        <key name="ecircumflex"/>
        <key name="ediaeresis"/>
        <key name="emacron"/>
      </key>
      <key name="r"/>
      <key name="t"/>
      <key name="z"/>
      <key name="u">
        <key name="u"/>
        <key name="ugrave"/>
        <key name="uacute"/>
        <key name="ucircumflex"/>
        <key name="udiaeresis"/>
        <key name="umacron"/>
      </key>
      <key name="i">
        <key name="i"/>
        <key name="igrave"/>
        <key name="iacute"/>
        <key name="icircumflex"/>
        <key name="idiaeresis"/>
        <key name="imacron"/>
      </key>
      <key name="o">
        <key name="o"/>
        <key name="ograve"/>
        <key name="oacute"/>
        <key name="ocircumflex"/>
        <key name="odiaeresis"/>
        <key name="omacron"/>
      </key>
      <key name="p"/>
      <key name="BackSpace" repeatable="yes"/>
    </row>
    <row align="right">
      <key name="Tab" width="1.5"/>
      <key name="a">
        <key name="a"/>
        <key name="agrave"/>
        <key name="aacute"/>
        <key name="acircumflex"/>
        <key name="adiaeresis"/>
        <key name="aring"/>
        <key name="atilde"/>
        <key name="ae"/>
        <key name="amacron"/>
      </key>
      <key name="s"/>
      <key name="d"/>
      <key name="f"/>
      <key name="g"/>
      <key name="h"/>
      <key name="j"/>
      <key name="k"/>
      <key name="l"/>
      <key name="Return" width="1.5"/>
    </row>
    <row>
      <key name="Caribou_ShiftUp" toggle="level2" width="1.5"/>
      <key name="y"/>
      <key name="x"/>
      <key name="c">
        <key name="c"/>
        <key name="ccedilla"/>
      </key>
      <key name="v"/>
      <key name="b"/>
      <key name="n"/>
      <key name="m"/>
      <key name="comma"/>
      <key name="period"/>
      <key name="question"/>
    </row>
    <row>
      <key align="left" name="Caribou_Symbols" toggle="symbols1" width="2.0"/>
      <key align="left" name="Control_L" width="1.5"/>
      <key align="left" name="Alt_L" width="1.5"/>
      <key align="left" name="space" width="5.0" repeatable="yes"/>
      <key align="right" name="Caribou_Prefs"/>
    </row>
  </level>
  <level mode="latched" name="level2" xml:base="common/qwerty.xml">
    <row>
      <key name="Escape"/>
      <key name="Q"/>
      <key name="W"/>
      <key name="E">
        <key name="E"/>
        <key name="Egrave"/>
        <key name="Eacute"/>
        <key name="Ecircumflex"/>
        <key name="Ediaeresis"/>
        <key name="Emacron"/>
      </key>
      <key name="R"/>
      <key name="T"/>
      <key name="Z"/>
      <key name="U">
        <key name="U"/>
        <key name="Ugrave"/>
        <key name="Uacute"/>
        <key name="Ucircumflex"/>
        <key name="Udiaeresis"/>
        <key name="Umacron"/>
      </key>
      <key name="I">
        <key name="I"/>
        <key name="Igrave"/>
        <key name="Iacute"/>
        <key name="Icircumflex"/>
        <key name="Idiaeresis"/>
        <key name="Imacron"/>
      </key>
      <key name="O">
        <key name="O"/>
        <key name="Ograve"/>
        <key name="Oacute"/>
        <key name="Ocircumflex"/>
        <key name="Odiaeresis"/>
        <key name="Omacron"/>
      </key>
      <key name="P"/>
      <key name="BackSpace" repeatable="yes"/>
    </row>
    <row align="right">
      <key name="Tab" width="1.5"/>
      <key name="A">
        <key name="A"/>
        <key name="Agrave"/>
        <key name="Aacute"/>
        <key name="Acircumflex"/>
        <key name="Adiaeresis"/>
        <key name="Aring"/>
        <key name="Atilde"/>
        <key name="Ae"/>
        <key name="Amacron"/>
      </key>
      <key name="S"/>
      <key name="D"/>
      <key name="F"/>
      <key name="G"/>
      <key name="H"/>
      <key name="J"/>
      <key name="K"/>
      <key name="L"/>
      <key name="Return" width="1.5"/>
    </row>
    <row>
      <key name="Caribou_ShiftDown" toggle="level1" width="1.5"/>
      <key name="Y"/>
      <key name="X"/>
      <key name="C">
        <key name="C"/>
        <key name="Ccedilla"/>
      </key>
      <key name="V"/>
      <key name="B"/>
      <key name="N"/>
      <key name="M"/>
      <key name="comma"/>
      <key name="period"/>
      <key name="question"/>
    </row>
    <row>
      <key align="left" name="Caribou_Symbols" toggle="symbols1" width="2.0"/>
      <key align="left" name="Control_L" width="1.5"/>
      <key align="left" name="Alt_L" width="1.5"/>
      <key align="left" name="space" width="5.0" repeatable="yes"/>
      <key align="right" name="Caribou_Prefs"/>
    </row>
  </level>
  <level mode="locked" name="symbols1" xml:base="common/symbols.xml">
    <row>
      <key name="Escape"/>
      <key name="1"/>
      <key name="2"/>
      <key name="3"/>
      <key name="4"/>
      <key name="5"/>
      <key name="6"/>
      <key name="7"/>
      <key name="8"/>
      <key name="9"/>
      <key name="0"/>
      <key name="BackSpace" repeatable="yes"/>
    </row>
    <row align="right">
      <key name="Tab" width="1.5"/>
      <key name="minus"/>
      <key name="slash"/>
      <key name="colon"/>
      <key name="semicolon"/>
      <key name="parenleft"/>
      <key name="parenright"/>
      <key name="ampersand"/>
      <key name="at"/>
      <key name="grave"/>
      <key name="Return" width="1.5"/>
    </row>
    <row>
      <key name="Caribou_Symbols_More" toggle="symbols2" width="2.0"/>
      <key name="period" width="1.2"/>
      <key name="comma" width="1.2"/>
      <key name="question" width="1.2">
        <key name="question"/>
        <key name="questiondown"/>
      </key>
      <key name="exclam" width="1.2">
        <key name="exclam"/>
        <key name="exclamdown"/>
      </key>
      <key name="apostrophe" width="1.2"/>
      <key name="quotedbl" width="1.2"/>
    </row>
    <row>
      <key align="left" name="Caribou_Alpha" toggle="default" width="2.0"/>
      <key align="left" name="Control_L" width="1.5"/>
      <key align="left" name="Alt_L" width="1.5"/>
      <key align="left" name="space" width="5.0" repeatable="yes"/>
      <key align="right" name="Caribou_Prefs"/>
    </row>
  </level>
  <level mode="locked" name="symbols2" xml:base="common/symbols.xml">
    <row>
      <key name="Escape"/>
      <key name="bracketleft"/>
      <key name="bracketright"/>
      <key name="braceleft"/>
      <key name="braceright"/>
      <key name="numbersign"/>
      <key name="percent"/>
      <key name="asciicircum"/>
      <key name="asterisk"/>
      <key name="plus"/>
      <key name="equal"/>
      <key name="BackSpace" repeatable="yes"/>
    </row>
    <row align="right">
      <key name="Tab" width="1.5"/>
      <key align="right" name="underscore"/>
      <key name="backslash"/>
      <key name="bar"/>
      <key name="asciitilde"/>
      <key name="less"/>
      <key name="greater"/>
      <key name="dollar"/>
      <key name="EuroSign"/>
      <key name="sterling"/>
      <key name="Return" width="1.5"/>
    </row>
    <row>
      <key name="Caribou_Symbols" toggle="symbols1" width="2.0"/>
      <key name="period" width="1.2"/>
      <key name="comma" width="1.2"/>
      <key name="question" width="1.2">
        <key name="question"/>
        <key name="questiondown"/>
      </key>
      <key name="exclam" width="1.2">
        <key name="exclam"/>
        <key name="exclamdown"/>
      </key>
      <key name="apostrophe" width="1.2"/>
      <key name="quotedbl" width="1.2"/>
    </row>
    <row>
      <key align="left" name="Caribou_Alpha" toggle="default" width="2.0"/>
      <key align="left" name="Control_L" width="1.5"/>
      <key align="left" name="Alt_L" width="1.5"/>
      <key align="left" name="space" width="5.0" repeatable="yes"/>
      <key align="right" name="Caribou_Prefs"/>
    </row>
  </level>
</layout>

I just removed a few mostly unused keys.

Then trigger the following script on vertical (left or right) rotation:

gsettings set org.gnome.shell.keyboard keyboard-type <your-keyboard-layout-name>

And trigger the same script with the normal layout for normal and inverted rotation.

For problem 2, write a script to toggle the keyboard first. The script shall look like this:

#!/bin/bash
device='AT Translated Set 2 keyboard'
oldstate=$(xinput list-props "$device" | grep 'Device Enabled' | rev | cut -b 1)
newstate=1
if [ "$oldstate" = "1" ]; then
    newstate=0;
fi
xinput set-prop "$device" 'Device Enabled' "$newstate"

While 'AT Translated Set 2 keyboard' is the name of the keyboard. Yours might have a similar name. Search for it with the command

xinput list | grep keyboard

and try to disable and reenable the printed devices. (Install 'Slide for Keyboard' first so you're still able to type in the command line)

You should put this script either on a hotkey or as a launcher in your applications list because you might not be able to reenable the keyboard if the script is on a keyboard shortcut.