If you think normal is hard, my goodness, don't even bother with hard. Enemies are ridiculous. 1 or 2 shots and you're out.
Like the others said, this is not run and gun. This game requires you to think, USE COVER, and make use of your teammates. I recommend the single shot firing mode as well on any weapon (it's more accurate). I personally used the MR-C rifle more than any gun in the game. I used it for just about every mission I could.
Always fire from cover. ALWAYS. Place your reticule over the enemy, or where the enemy comes out, then when they stop firing, pop out and headshot them.
Also, if you're engaging multiple enemies, use your teammates. If someone is giving you a hard time, assign your squad to take him out. While doing so, you can take out other targets that may be a threat to your teammates WHILE IN COVER.
And yes, use your drone as much as you damn well can. Letting that thing spot enemies for you makes the game sooooooooo much easier.
Also, no. If you turn off the 360, you start the entire mission over.