Today is month of january going on, my question is will time value in OTM options decrease as fast in feburary contract as it decreases in january contract?

General
2

Well. Checked in option calculator, keeping rest all equal; if theta value of jan series is -3, then for the same strike price feb series theta value comes to -2.7. So feb series time value decreases slower compared to jan series.

3

No. Since February contracts are having 28 more days than Jan expiry, the option price will fall slowly in Feb contract than Jan contract (talking about time erosion only).