Q1) Will the miner always (in theory) abort attempting to mine the empty block as soon as he can start working properly on the new block, but now including the new TXs in it?
I presume he would, looking for a greater reward from the non-empty block, and dedicating all his hash power to it.
Since the miners are now almost all mine whiting a pool, the pool needs to generate a new block template and send new work to the miners that are already working on an empty block template, so it is likely to delay that for a while ( probably a few seconds) to allow shares coming from those miners before sending the new work.
Also since there is nothing in the protocol that governs this process, each pool is likely handling it a bit differently
Q2) Do all/most of the miners try to mine empty blocks? or are there some known big mining players that oppose the practice as far as you know?
When I made my analysis on the subject, I found that all pools mined empty blocks except for Kano.is, kano publicly stated that his pool code won't send an empty block template to miners unless his mempool is empty which is more like 'never'