If I am correct Binance has started allowing deposit and withdrawal from today.
Withdrawals are still suspended for me, and I've been checking frequently as I want to get some NEO off Binance as soon as I can.
As far as Binance's hack affecting the price of bitcoin goes, I don't really think this rise had anything to do with it. There have been big exchanges that have gotten hacked in the past (Cryptsy is the one coming to mind first), and no one exchange's hacking or failure or whatever can influence bitcoin all that much. Mt. Gox was a big exception to that, because if I'm not mistaken they held an enormous percentage of the total circulating bitcoin at the time, but that's not true of any exchange these days.
Binance might be very popular and very big, but there are a lot of other big exchanges today, unlike in 2013. That's actually comforting to know.