If I put a headphone jack (without Mic) in my Android Phone socket, which is with-Mic, will it damage the phone? It might get sort-circuited?

No. Headphone sockets which cater for microphones are designed to accept normal stereo headphones without microphones as well.

The only problem is the other way around: regular stereo headphone sockets don't always play nicely with triple-banded (stereo + microphone) plugs as they weren't originally designed with those in mind although no damage occurs if you put a triple-banded plug into a purely stereo socket: the worst that happens is the sound doesn't come out correctly. But newer devices with no use for a triple-banded plug are built with sockets which will still work fine with both types.

No of course it won't. Headphones are completely compatible.