According to Rambam, whoever learns all day and lives from charity gets no place in olam haba.
If the money was given by a donor with the intent to allow learning, it is ok. Often times though the monies for learning and tzedakah are mixed.
Welfare is charity.
Ideally, even rabbanim should not be paid. Religion is not a business to make money. Well, it us. But it is not supposed to be.