there is nothing wrong with GitHub so there is no point in creating another site for listing BIPs which is why there are none available. some very popular BIPs might have been explained elsewhere also such as BIP32 and they also are linked in bitcoin wiki page. but there is no dedicated website listing all other than GitHub.

there is no rule saying you can't post link to another website here in this board or any other board, as long as it is not for spamming or advertisement.

not exactly "approved". BIPs are just "proposals", some of them are already part of bitcoin consensus (if they are consensus related, if not they are there and you can use them or not like BIP178), some are rejected, some are deprecated by a new version, some are withdrawn,...
check out the "status" column of the table at the bottom.
withdrawn: https://github.com/bitcoin/bips/blob/master/bip-0012.mediawiki
replaced: https://github.com/bitcoin/bips/blob/master/bip-0020.mediawiki

basically any proposal that is "ready to be proposed" is placed in there. if they are in early stages, incomplete, need more testing,... they are discussed elsewhere like on mailing list and usually reside in repository of the proposer then added to the list when they are complete.