Thank you for the answers. It became clearer now.
The covert form involves finding multiple merkle roots which collide in the last 32 bits.
This actually answers question 4.
I guess, that since they need a special merkle root, it may happen, that an empty or almost-empty block provides a necessary merkle root, so they just keep mining such an empty block until it is mined or an optimized merkle root found for a filled block, whichever happens first?
Provided with the answers, I would rephrase the sentence, that asicboost optimized miners mine several blocks at once. Some of them may happen to be empty or half-empty. They don't exclude underfilled blocks from the set because it would decrease efficiency of their optimisation. Once they found a set of colliding merkle roots, they mine corresponding blocks, until one of the blocks is mined or another set of colliding roots (for better blocks) is found.
Possibly, but given that empty blocks still happen without asicboost, it isn't really an indicator of much.
So, in my opinion, increased rate of empty blocks does increase our suspicions. Although it isn't a proof of course.