The most exchanges have issues through high demand right now.
It is really annoying but even websites need to adjust to this high demand.
I personally did not have any problem with deposits and withdrawls on Bittrex.
Normally done in some Minutes.

More Problems I am having to buy coins.
On Litebit I experienced 2 times (Bitcoin price drop)
That there were out of stock and you couldnt buy anything for days.
This is really annoying. So I feel u all.

Anyway Bittrex is in my opinion legit.