RE: is it ok to keep my eos on the bitshares exchange has open.EOS when the crowdsale ends?

I would say no, there has not been an announcement starting hey will support the mainnet swap and they are not supporting all the airdrops for sure.

Get your tokens into a wallet that you have control over the private keys for, then get your wallets address registered so you can take advantage of the airdrops coming soon.

If you really want to keep your EOS on an exchange, Binance or Bitfinex are honoring both the mainnet and airdrops.

Here is a link on how to register if you choose to get off the exchanges.

https://steemit.com/eos/@aclarkuk82/eos-registration-how-and-why