The problem with Heal is that it doesn't scale well once you get to the higher levels. It's designed to do healing based on a level 18 base HP bar, but that's not taking into consideration any items in the post-18 game. Plus it's countered by reduced healing effects like Ignite, Katarina's Death Lotus, Miss Fortune's Impure Shots, etc. While all heals are affected as such, in this case it's a tad more game breaking since it's eating up one of your summoner slots.
Revive is generally a poor choice due to the fact that it requires you to be dead in order to use it. Obviously you want to avoid being dead in the first place. While you generally can't avoid at least a handful of deaths in a game, you don't want to count on Revive being used as quick-back from death, compared to another skill which could have prevented that death in the first place.
That all being said, there are a few champions that can utilize these skills particularly well. A lot of support characters can utilize Heal quite well like Taric, Soraka, Sona, Alistar. Combining Heal with their built-in heal spells can provide an inordinate amount of burst healing which can be deceptive to the enemy team.
Revive is a good gimmick choice for a Twisted Fate or Pantheon playing mid to push the lane early. Once you're 6, go for a skirmish with your 1v1 opponent. If you win, great! But if you die, no big deal. Immediately revive, buy (be ready!) and ultimate back in, using your Gold Card (TF) / Shield Bash (Panth) to stun and finish them off. You have the speed boost from Revive so they wont escape, and now you have a good 15-20 seconds to push the tower. If you're well organized, you can have your jungler come help, or a sidelane move off to come finish the tower if you cant, keeping a strong 2v1 in another lane.
Additionally, Revive can be extremely strong late game when respawns are 50+ seconds long. You can turn a potential tower / inhibitor kill into nothing after a bad teamfight that's left you with few to no allies left. However, usually you don't want to ASSUME this is the fact, because you could have avoided that situation with a different summoner skill in the first place.
Basically, they're situational abilities with their place, but generally they're overshadowed by some of the more popular abilities.
The new summoner icons are to be unlocked via achievements. However, achievements haven't yet been released in LOL (You'll find the 'not yet accessible' tab in your summoner profile). There have been quite a bit of rumors lately on what the achievements would be, but I still haven't found anything serious on the subject.
Conclusion : Wait and See
Best Answer
It all depends, the summoner spell cleanse can always be cast, even when stunned. The rest of them are stopped on Silence, Stun, Charm and Fear. But aren't stopped when your snared meaning you can't move but can still use your abilities and spells.
Edit: Except Flash, you can't use Flash while snared just as Patrick Stalder noted.