OS: Ubuntu 18.04.3
Tested in Ubuntu 18.04.3

Workaround

QP1. Keyboard Layout:

Say, If you have 4 keyboard layouts, they will be shown in the file /etc/default/keyboard. The order in this file will show you at login.

XKBLAYOUT=kr,cn,fr,us
XKBVARIANT=,,,
BACKSPACE=guess

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QP2. Mouse Sensitivity:

If I understood "Mouse Sensitivity" Correctly, Mouse Speed in the below Image.

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This can be achieved with below command

sudo -Hu gdm dbus-launch gsettings set org.gnome.desktop.peripherals.mouse speed '1.0'

Change the value in above command between -1.0 to 1.0 slow to fast

Reboot is required to take the effect.

QP3. Login Screen Resolution:

There are related Questions for this..

Ubuntu 18.04 login screen Display settings
How do I change gdm3 login screen resolution?

following the first link above, I could successfully configure Login Screen Resolutions..

This Solved my Isuue:

Go into Settings > Devices > Displays and configure your monitors the way you want for your login screen (in your case, internal laptop display disabled). Click the "Save" button when done.

Copy your user's monitors.xml file into the home folder for gdm user.

To copy the monitors.xml file, open a terminal and perform the following:

sudo cp ~/.config/monitors.xml ~gdm/.config/monitors.xml
sudo chown gdm:gdm ~gdm/.config/monitors.xml

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The elusive login screen settings you were searching for are stored here:

/usr/share/glib-2.0/schemas/org.gnome.desktop.peripherals.gschema.xml

The reason you can't change login screen settings for keyboard and mouse is explained in a bug report:

The login screen runs as user 'gdm' which is not privileged. That means it has no access to retrieve your personal settings until after you have entered a password. So it uses the system defaults.

You should subscribe to the bug report. The bug was filed June 28, 2018 but only has one subscriber as of December 21, 2019.


Setting Grub resolution

The key to changing your login screen resolution is changing grub's resolution:

  • How to change the login screen resolution in Ubuntu 18.04

To summarize the link, in /etc/default/grub:

Use the down arrow or Page Down until you see the line that looks like this:

#GRUB_GFXMODE=640x480

Below that line, enter the following, substituting the 1920x1080 for a supported resolution:

GRUB_GFXMODE=1920x1080
GRUB_GFXPAYLOAD_LINUX=keep

Setting default keyboard layout

To set the default keyboard layout change /etc/default/keyboard as described here:

  • How do I change the login manager's keyboard layout?