Short answer - yes, it is possible.

To avoid that you may need to think about the barriers that make this scenario less likely:
1. Frame your solution such a way that it will be easier and more profitable to cooperate with you than copy
2. Select for begin small enough niche, so they don't bother
3. Get a patent for you technology

You may also try to ask them to sign NDA and Non-compete agreement before presenting the idea, but it will be extremely hard to do.

Yes this is indeed possible. Like most things in business this is a cost benefit analysis. A company will assess if the cost of acquisition outweighs the cost of implementation. Also the only way your app would be a candidate for acquisition is if your product is truly aligned with their overall strategy. The best you can do is patent and copyright where appropriate, and insure that your product is so far ahead that it would not be worth playing catch up.

Of course. This is very risky since they also might have some patents.

If it's just an "addon" or a feature on top of an existing very complex app, I would stay away from it. You would have to reinvent the wheel, build the full scale product, get traction and then try to sell it to them.

Most companies don't buy features, they just rebuild them. Unless you can product it with a patent which is very different right now in the software space.

Let me know if you want to have a call and if you have more questions.