IIRC, M-banka and FIO banka were offering a remote account opening some time ago; but I am afraid for Czech residents only. But especially M-bank is perhaps worth checking, it is a (very small) multinational so it might be possible to use (on-line) their branch in another country (depending of your residence) to obtain a Czech account. Otherwise, Intergiro can provide Czech IBAN (or, to be exact, a possibility to execute local payments in CZK) under some circumstances but I am unaware of details. Similarly it might be posible with Zen or some another Lithuanian EMIs but I definitely did not recall...
To the best of my knowledge, I am unaware of any Czech
EMI that offers personal IBANS. AFAIK, there are 2-3-4 offering payments processing but with shared accounts. But IMO they are relatively popular with the businesses because of FX rates.
Correct.
It depends on a particular bank but I would not use the word “very“. I do not have a lot of personal experience with Czech banks in the last years but I would say that for example
KYC/AML burden is roughly the same (note that the vast majority of Czech banks are just daughters of western banks).