1. No, it is p2p, so unless every single person running the bitcoin client goes down (see
here for how many that is), then the network it up. You cannot DDoS it.
2. To sign or verify a message to an address it is free.
3. Resetting Blockchain in MultiBit just refreshes it, you still have your coins as long as you have the private key. (Refreshing blockchain does not delete the key)
4. It does not connect to a single computer, it connects to many computers around the world. Not one person owns it. If you run it on your PC, then you will become part of the network.
5. Your computer, and CPUs in general will be able to generate very little bitcoin, now that ASICs are on the market. If you really want to look into it, see
this.
6. If you don't post for 2 weeks, then you will not get any extra activity.
7 & 8. To see how activity is calculated, see
here.
I hope this helps, and welcome to the community!