Given that you can buy these Bitcoin miners and they are specialised ASICs for calculating SHA256 hashes in a specific way to find the first acceptable nonce, it's unlikely that Bitcoin mining hardware can be repurposed in this way.
On the other hand a manufacturer capable of designing and producing SHA-256 chips could be also capable of designing and manufacturing $other_commonly_used_hash_algo chips allowing for brute-forcing $other_commonly_used_hash_algo encoded passwords. The same manufacturer/design team could also probably prepare $popular_block_cipher chips. So, while BTC miner chips would not be useful themselves, having an industry capable of creating those chips is.
Correct. The vast majority of bitcoin miners are specialised ASICs for calculating BTC related hashes explicitly, and nothing else. Optimised for efficiency of the task at hand.