There are different factors that influence the percent chance of hits.
Range (in some cases more than others. Shotguns have a awefully short range and you have to be directly before the enemy to get a good shot), cover (half cover and full cover give different advantages. They decrease the chance to get hit by an amount unless youa re flanked), line of sight (it should be noted, like kasnavada already said, full cover BLOCKS line of sight but you can still get hit if the angle is right. And yes, aliens are clever enough to get around that angle), firing angle (in the expansion more as in the base game but lien of sight is still important and therefor the angle to your enemy. Also, flanking) and some other stuff like buffs and debuffs.
Alien weapons have, especially in the higehr difficulties a rather high success chance and I agree that this is a little off. But the tag "Impossible" should give you a hint that the game really gets impossible. On "classic" the game gets managable and it depends on you and the full use of cover, buffs, debuffs. If you miss all that... well, than the fault is on your side, not the game. XCOM is very punishing, has always been. One mistake and you will mourn over your full armed soldier.
Liek I said above, full cover can block line of sight and the right use can give you a big advantage. Set your soldiers on overwatch and let them come. They have to move to the right angle and while moving enemies are hard to hit, they still loose the cover bonus while in motion. Some enemies cannot even use cover at all (but have some other bonuses to make up for that)!
I think the game is manageable. And now I want to play it again, dman you all!