Local LAN, yes. Samba, yes, with some apps (many of them free). FTP definitely (again with free apps). And I didn't know so I just checked, and there are a lot of free SSH clients.
Don't buy the cheap Chinese tablets, though. Some aren't what they claim to be (like hardware barely able to run version 2.3, but running 5.0, so you can barely squeeze one app into it), tabs for which no one has any information, so if you need help, you throw the tablet out and buy a new one - that sort f thing. Name brands cost more, but places like
XDA Forums have developers who do what can't be done to some of these devices, so they know them pretty well, and can help you fix anything but broken hardware. (We don't do to badly here ourselves, when it comes to helping people getting name-brand devices up and running again, but some of the people over there seem to know the devices better than the people who designed them.)
As far as connecting to a TV, if the tablet can run
Chromecast (
Chromecast mirroring), it can mirror to a TV as long as there's a local wifi signal. And Samsung devices can mirror to Samsung TVs without anything additional.