The TeleType Consoles in linux can be switched by Ctrl + Alt + F(#TTY).
How many such TTY's can linux have at a time? Is there even a limit?
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You can only run a virtual console (VC) on a tty device that exists. By default, Debian Linux ships with 64 such device files (/dev/tty0 through /dev/tty63). Other reading suggests that the limit in the kernel by default is 256 of these, so it may be possible to create up to /dev/tty255. If you need more than that, you'll probably have to recompile the kernel.
The more practical limitation, however, is how do you actually use that many VCs? LeftAltF1 through LeftAltF12 will only get you up to VC 12 on most keyboards (10 on others). To extend this number, most Linux systems ship with RightAltF1 through RightAltF12 mapped to VCs 13 through 24. Beyond this, you can do your own keyboard mapping, which you can read about here if this is something you're interested in doing.
You can also use Altleft or AltRight to cycle through all VTs. And the
chvt command can be used to directly change to any active VT.