Termites will put a lot of effort into breaking through something that stands between them and food or water, just so long as the prize justifies the effort required.  Plaster (drywall etc.) is no barrier.  Mortars slow them down, but lime mortars are readily penetrable while mortars with a high cement content may not be excavated.  Good quality concrete cannot be excavated BUT cracks in poor concrete may be opened with ease.  Autoclaved aerated concrete (those lightweight bubbly blocks) were readily penetrated in my field tests.  Concrete (cinder) blocks sometimes

Yes, termites do bite people if you get them angry enough.  With most species they have to find the thin skin between your fingers (or similar) before you'll even notice.  They don't set out to bite people, but they will bite in defense.  Bigger species like Mastotermes, Macrotermes and some dampwood termites are much better at being noticed.

Yes.  "White ant" is another misnomer used to label termites.  They're not white (cream is as pale as they ever get) and they are very different to ants.  Ants belong with bees and wasps whereas termites are really social cockroaches (did you just shudder?).  Please don't say "white ant" unless you were born before 1950, have really bad eyesight or have to so as not to cause offence.

Depending on where you live, it may well be that the termites in your garden are no threat to anything.  There are lots of species that never, well mostly never, behave as pests.  In my garden a Nasutitermes and a Porotermes pose no threat to my home.

This is a tricky one, and this answer is only for subterranean termites (not for drywoods and not for dampwoods).

Let's say the termites are in your neighbor's house.  If baits or another colony-killing method is used, then the risk of that colony to your house is gone.  If they just repair the damage or poison the ground with a repellent chemical (like bifenthrin), then the termites may be 'pushed' towards feeding at your place.  That isn't good.

They don't. 

There's no simple answer to this one.  It depends. Species, life-type, wear and tear, colony health--all these things affect the potential for a long life.

Termites have no malice, so it is definitely nothing personal.  Their needs are simple. Food and shelter are almost always freely available for them in what we build. Water is the big issue and often we can build termites out by making it harder for them to get water so they can eat.