Is it normal for a poker room to require copies of documents and even from your bank account?
Many (if not all) poker rooms have different restrictions with which players must comply. For example, you mustn't be underaged, or you mustn't be from a country where online
gambling is illegal and etc. Upon account creation you can specify any info you want but the only way to ensure that info you provided is true is to check it via some documents which confirm your identity and other stuff (like age).
Though i can't say when verification procedure is usually applied;
poker stars, for example, hasn't yet requested any documents from me despite the fact i played
freerolls for like a month and won a little bit of money (but i haven't withdrawn any money from there and haven't made any deposits).