How can I make gnome-shell treat both monitors in the same way?

14.04

In later versions of Gnome, you have to open gnome-tweak-tool and, under "Workspaces", change the "Workspaces only on primary display" setting.

I could not find the /desktop/gnome/shell/windows key mentioned by Martin, but the source he's quoting says to run:

$ gsettings set org.gnome.shell.overrides workspaces-only-on-primary false

This fixed it instantly for me. Thanks, gregcor (the source).

Setting workspaces-only-on-primary false (using gsetting, gconftool, GNOME Tweak or whatever – see all other answers) only solves the first problem:

Gnome-shell seems to like to leave one monitor as "fixed" when you switch workspaces.

For the second problem

Additionally, there is no preview in the Activities view of my secondary monitor.

there is a GNOME extension called Multi Monitors Add-On that Just Works™. (See also How do I install and manage GNOME Shell extensions?)