You can deposit funds with almost all the altcoins that exists (only those who bittrex have listed)
But no, you are not able to deposit funds via wire bank in there, only with altcoins.
1. To buy from bittrex do i have to start with bitcoin/eth before I can buy anything or can I buy straight away with real usd in my bank?
It depends on the altcoin that you are trading, NEO is only exchangeable for bitcoin - usdt- or ethereum.
There are other altcoins that are bigger that allow theirselves to be exchanged for xmr, litecoin, etc.
2. Once I buy say Neo, once it goes up can I trade it at bittrex for another coin besides eth or bitcoin down the line or do i have to trade it for bitcoin/eth?
If you are going to do daytrading, then dont move your funds everyday because you are going to be raped with the fees, if you are going to hold, then buy an offline wallet (A trezor - ledger)
5. Do you put your alt coins in a hiding place offline so a hacker cant steal it? If so whats it called