2.  Is F2Pool/AntPool more likely to produce an empty block when mempool swells?

...I don't see why the answer to Q2 would be yes for any reason other than the previous block is more likely to be large when mempool swells (i.e., mempool is not the cause, just correlated).

As miners have created larger blocks F2Pool expirenced high orphaning (>4% according to them); they responded by adding software to mine without transfering or verifying blocks to avoid delays related to transfering and processing block data. Contrary to your claim-- the blocksize limit stems the bleeding here. Their issue is that large blocks take more time to transfer/handle and that they're falling behind as a result. Making blocks _bigger_ would not help this problem, it would do the _opposite_. If a miner wanted to avoid any processing of transaction backlog they'd simply set their minimum fee high and they'd never even mempool the large backlog.

Reasonable minds can differ on the relative importance of difference considerations, but when you're falling all over yourself to describe evidence against your position as support of it-- redefining F2pools crystal clear and plain descption of "large blocks" as their source of problems with the technically inexplicable "full" that you think supports your position, it really burns up whatever credibility you had left. That you can get away with it in this thread without a loud wall of "WTF" just shows what a strange echochamber it has become.