1. Reaction fire IS working. You either did not activate it or alien didn't spend enough TUs within field of fire of that soldier to trigger it. It's a common tactic for them to walk behind your soldier before firing so he doesn't see them firing, thus not triggering RF. Positioning, proper choice of weapons and mode for RF will help.
2. Flashbangs. I've noticed that when they explode exactly on same cell as alien is, they fail sometimes. If they explode next to alien they usually work. Also, use the same trick as aliens to avoid their RF if you can. The game isn't supposed to be easy, use some tactics and you'll do okay.
3. You need to do some compromises, especially early on when your soldiers have just few missions. But even starting soldiers can carry armor, weapon, sidearm, one reload for both, IR goggles and couple grenades, barring some heaviest weaponry. Medikits are usually reserved for troops with lighter weapons like assault rifle, but if you select your troops properly, troops with lighter weapons will be able to carry full backpack within dozen of missions. Of course, then new, heavier armors become available and you'll need more trained soldiers to carry the same gear with heavier armor. Learn to do compromises, think about what you really need (my soldiers don't need more than one reload for mission barring extreme circumstances).
4. They're fast, but dumb. You also have the benefit of medikits and after mission, hospital that now heals quickly. Little tactics are enough to get casualty rate to less than 1 per mission. This isn't supposed to be walk in the park.
And finally, learn to use less exclamation marks, question marks and caps. People will take you more seriously.