There is no deadline for selecting projects nor is there any restriction on the number of projects you can contribute to; you can also switch between projects as much as you want. The only necessity is that you should have made at least one commit before mid-term evaluations.
No, KWoC is a program which aims at helping participants learn how to contribute in the open-source world. This activity prepares you for various open source opportunities such as Google Summer of Code, Rail Girl's Summer of Code and Outreachy.
Nothing makes us happier than people spreading words about open-source; to begin, you can like our facebook page and increase awareness about KWoC in your college; nothing works better than word of mouth.
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?".
Other program similar to KWoC are GirlScript Summer of Code organised by GirlScript India. If you meant 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 projects you choose, more time in conversing about the work.
Participating in Open Source contribution improves your skills of software development and of a particular programming language. Depending on your project, you might be able to use some algorithms too. But you should not be direct improvement on your competitive coding skills.