You're mistaken. The difficulty would re-calibrate and it's business as usual.

However, if China or some other government compelled miners to sign invalid transactions, this would have a big impact. This is a weakness of proof-of-work secured coins (note that they also have many strengths that proof-of-stake coins lack).

EDIT: I was unclear what I meant by "this is a weakness of PoW" -- the energy signature of concentrated mining operations make them easy for governments to find.

I don't think a transaction would just become valid if a miner (who mined a block) signs it. Each participating node will independently verify the chain for signatures of transactions before it accepts the latest block. So a miner who mines a block with invalid block will just waste his efforts on it. The chain length is used a proxy to find out a valid chain only when two competing chains have valid blocks throughout but have different lengths.

Depends on how much the hashrate changed: http://bitcoinandtheblockchain.blogspot.com/2017/08/chain-de...

You are correct, this seems like a defect that should be addressed.

it depends on what you mean by "invalid transactions". If you mine a block that doesn't follow the rules, the rest of the network will just ignore it, and so you've wasted your computation.