When you press Ctrl+Alt+F7, you're switching to a different
tty or virtual console.
These virtual consoles work much like a Terminal, such as
xterm, except they aren't loaded by your Windows Manager, and you will likely need to login to them. Be warned, if you login and fail to log out, that
tty will stay active and someone else can just switch over and use it.
That means that just like you can use other tools, such as
tmux to multiplex your terminal, you can do so in your
tty. One of the benefits from using one of these multiplexers is that they support multiple 'tabs', have ways to have multiple shells or terminals in a single
tty or terminal window (your goals) as well as support resuming of the session later. There a lot of guides on how to use both
tmux, but I would recommend you taking a look at The Tao of tmux, as that is very detailed and doesn't assume you know a lot about everything else. There are images there that will help explain how you can split your
tty into multiple terminals, and how to switch between them.
If you wish to automate something for when you login, you will want to look into how sourcing files at login, such as
~/.profile and other shell initialization files work, while also looking into how others have solved similar problems.
Without more specifics, I hope that this helps explain that you can use a multiplexer that supports splitting to accomplish your goal.