I am fairly new to cryptocurrency and I'm learning a lot as I go. I use the Exodus wallet for my main coins but I recently decided to purchase some altcoins using Bittrex. I got that figured out but now I'm not sure of the best way to store them. I know that you're not supposed to use exchanges to store coins for long term. Each of the altcoins that I purchased has a desktop wallet.

Question 1. Do I really need to install a desktop wallet for each coin to keep them safe?
Question 2. Once I send the coins from Bittrex to the desktop wallet address, can I just close it and not open it for a while?