I will also add the disclaimer that this is all just my experience/opinion. No bibles of the herpetological variety need be thumped.
1. I generally feed in the tank. No aggression problems, no impaction/substrate ingestion problems (though I also make sure they aren't eating directly on the aspen--instead on top of a hide). I'll sometimes pull them out and feed them in a separate container, if I'm wanting to get a weight or watch them eat for funsies... Whichever works for you. They don't really care either way. (... Usually, anyway.)
2. Remove mouse from bag, toss mouse in room temperature water, walk away for 10-15 minutes. Come back, replace now cold water with warm water, walk away again for a few minutes. Make sure mouse is thoroughly thawed, fetch hemostats, give to snakes. You can also put them in the fridge overnight, set them on the counter for a few hours or so, or, as has been stated, put them in a baggy and then into warm water. There's a dozen ways to thaw mice. Just don't try to thaw them in the microwave. Yuck! (Oh and I don't have a designated container. I usually use the old spaghetti sauce jars, which my brother uses as drinking glasses. I figure the dishwasher gets them clean enough. And there are a lot worse things to eat after than mouse juice.. Like raw chicken, or, well, my brother. I have yet to get salmonella or any other icky thing from this routine. Though I do understand and respect others' choice to not use their eating utensils for reptile chores.)
3. If you mean having the snake mistake your fingers for food because they smell like mice, yes, that is a big concern. That's actually why I finally started using hemostats/tongs to offer food. That and snakes don't always have great aim.
If you mean, though, that the snake will smell you on the food, associate your scent with the food, and later mistake you for food (what I originally thought you meant), not really. I've never, ever had a good snake turn "mean," much less in any way that can be associated with food, and my preferred method of checking to make sure the food is completely thawed is to "massage" it bare-handed and feel for cold spots.
4. Honestly, the worst part of a snake bite is the shock. My first bite was from a 6' rat snake. Once I got past the shock and horror of the whole event, the pain was actually pretty minimal. (It should be noted here that I'm a total sissy.) From a corn snake, you have quite literally nothing to worry about. (And, no offense to this friend of yours, but she must be an even bigger sissy than I am to think a corn bite hurts at all, much less "like crazy"!)