Voltage and Amperage in relays
1) Driving 35 amps through contacts rated for 10 amps is a great way to kill the contacts. 

2) The contacts will fail either by welding shut or by "burning" so that they can no longer make contact. Which is more likely depends somewhat on your load. If your load is purely resistive or has a turn-on surge (like incandescent lamps or capacitors) then welding is the more likely failure. If the load is inductive (like a motor) then burning the contacts when you try to open them is more likely.

3) In the terms you're asking - no.

4) Yes. (With this exception - if the NPN can be used to interrupt the current flow before the relay is opened, it will prevent burning the contacts. Of course, if you can do this, why are you bothering with a relay?)

5) Whoever said you can push 20A through a 10A relay is giving bad advice, and the concept that "is just the relay output will not exceed 10A" makes no sense at all.

You need a beefier relay.