Invuln tank build questions

Both tough and weave will be extremely useful to an invulnerability tank. With tough you will cap your smashing and lethal resistances (90%), and weave does very well in stacking with your defenses in tough hide and invincibility. You can 'soft cap' your smashing and lethal resists without tough, but that requires unstoppable which is not permanent and has a punitive crash when it wears off. While it's possible to cap defenses in certain situations without weave, doing so is extremely expensive and, in my opinion, impractical and inefficient. Put simply, yes you'll benefit in a noticeable way from the fighting pool.

Aid self is an alternative, though it doesn't compare as favorably in most situations to tough and weave. It can fail to heal and occupies a not insignificant portion of your time in a fight doing something other than fighting. The main selling point to aid self is that it, as a heal, does not care what type of damage you've taken making it more useful for covering your weaker points such as psionic damage, as opposed to capitalizing upon your strength by taking tough.

Yes, there is, but it involves IOs, and won't help too much. You can definitely slot for it, but it's really going to depend on what you're after whether it's worth it or not.

I'd suggest you read my guide to the first 20 levels for a good solid foundation to build on. From there it depends on what you want to do, although if you're just starting in the game I'd not worry about my more advanced soft cap guide just yet; you have enough to learn without heaping too much on you at the start.

An Invuln tanker is perfectly capable of handling nearly anything in the game without an IO set build... it just gets easier to do with one. Due to the complexity of IO builds though I rather strongly suggest you stick with DO and SO enhancements for now until you have your feet under you and aren't still learning the ropes.

Oh, one minor thing, as a tanker you're Invuln/Dark; a Dark/Invuln would be a scrapper or brute. (Primary/Secondary is standard terminology)

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Oh, on the Psi issue my advise is to ignore it; Psi damage is extremely rare and in all but maybe a half dozen missions I can think of, all in the 40's, what Psi exists is pretty minor damage. Dull Pain and the occasional inspiration should do you for 99% of all the Psi you encounter.

Another point is that you really can't get a meaningful amount of Psi resistance anyway so I don't see the point in going to extreme lengths looking for it.