I just started trading crypto currency. This is my first time to trade. What I did is just a self study. I read everything about crypto and trading and watch videos on youtube. Some did not makes sense

One question in my mind is , is it safe to just store my bitcoins and other coins that I bought on BITTREX? I have a blockchain account but the fee when sending and requesting withdrawal is quiet high. So I decided to just store it on bittrex. For the other crypto currency, I only have ETH Wallet.
Thanks for the help.
Personal opinion from experience: it is not safe, especially if you have an unverified account.
Exchanges often run into liquidity issues that cannot be predicted beforehand until it is too late. The regulation on cryptocurrency trading can tighten up all of a sudden, meaning that you can't withdraw money. Or your account could just be suspended without reason.
Too many things that could go wrong. I definitely suggest downloading the wallet for each of the coins you hold, it's worth the hassle.