Stratum mining, jobID and stale/rejected shares Let's imagine following situation:

I've got a job from stratum pool, miner found golden nonce and sending it over the pool. 

While waiting for pool response, miner found another satisfying nonce within the same job.

Question1: will stratum mark second nonce as stale or reject it when submitted to the pool?
Question2: if I found another nonce by increasing nonce2 field for the same job ID, will it be accepted by the pool?
This depends on the Stratum implementation. There are many. The Stratum protocol does not require implementations to accept or reject the second proof of work you send in with this scenario.

Most likely the pool will quickly send you new work data after you send in the block solution. After that it will receive your second proof of work and it will be rejected as stale.

There will always be some stale work as new blocks are found.

Clients should submit their data as quickly as possible. Pools should distribute new work data as quickly as possible when new blocks appear, to reduce the amount of wasted work. Pools should also distribute blocks to other pools as quickly as possible, to reduce the amount of orphaned blocks.