Now they tell me that they have to manually check it and that it could take a month or more and this if it finally gets credited, maybe I "lose" my coins, they don't assure me that it will be credited even having blockchain tx id proof.WTF
This is unacceptable, avoid this exchange at all costs.
Bittrex's trust has really taken a hit in the past year or so.
Is there anything special at all that may have happened that resulted in this? If you deposited to the right address, above the minimum deposit(obvious in this case), and have all the correct info in your deposit, then there is no reason for them to have to hold your funds in their custody for so long until you actually get a chance to trade with funds that's rightfully yours. They probably don't have the best support system out there as well.
Do update us on the situation as it progresses. Hopefully, you're able to sort this out sooner rather than later.