The obvious answer is that yes, it will both impede his channeling and it will limit what he's able to do, as well as limiting what LTT can do. The issue of learning weaves with hand gestures has been well covered via the AS, and by all accounts it's not an insignificant issue. Much as with the sword, Rand will need to relearn weaves previously used via both hands (or just the left hand). As for LTT, we've only had the one "take-over" and LTT made it clear he wants use of both hands to channel, so the assumption being that it will affect him just as much.

On a related note, some have argued that Isshy used the Manor attack in order to evaluate the extent of LTT influence on Rand's actions. Seeing the result, Semi was then sent to interrupt LTT's assistance, via the removal of one of Rand's hands. Not sure I buy this, as it would seem very peculiar for Isshy/Semi to have the foresight of Rand's decision to take Min to the meeting, have her right next to him, not be holding Saidin, and finally to expect the type of internal struggle that prevented Rand from grabbing saidin in time to avert the fireball. The circumstances leading to the fireball and Rand's burned stump would not appear to have been that predictable. This doesn't discount the idea that Isshy was behind both attacks for whatever reason...just not for the specific reason of giving Rand a burned-stump.

But back to your questions, yes it will impede him. How much? We'll see. I would guess the simpler the weave, the easier to relearn and vice-versa. As noted above, it should also limit LTT and therefore also limit his teaching abilities. LTT will have to "relearn", if possible, a given weave himself...perhaps he and Rand will learn together?

I tend to think Rand's hand is done for good...his body is breaking down which ties in with the mountain of symbolism attached to his role. As for Elayne's role via Min's viewing? Sorry, no good answer here. It's possible I guess, RAFO!