There is absolutely no selection criteria for students. You are selected in the program as soon as you register. So you don't have to ask your mentors "How to get selected for your project?", but instead go ahead with "How can I contribute to your project?".
If you mean similar to KWoC, then this is the second time anything like this is happening in KGP. If you mean similar to GSoC, then look around, there are plenty of them e.g. KDE summer of code, Outreachy, Rails summer of code, etc.
GSoC requires 40 hours per week in summers. For KWoC, you may give 1-2 hours daily and that includes conversation with your mentor(s). More the project you choose, more time in conversing about the work.
This question is very debatable. Participating in Open Source contribution will improve your skills on software development and of a particular programming language. Depending on your project, you might be able to use some of the algorithms too. But direct implications on ICPC will not be very helpful.