Some questions about how to start...
1. I downloaded a Blockchain.info wallet to receive my Bitcoin in. Is this a safe wallet?
It's safe in that it's a legitimate company and you have your private keys, yes. However, you would be much better off going with a normal software wallet like
Electrum to start off, because Blockchain.info is very poor at fee estimation and is known for regular bugs.
2. From what I have put together so far, the way to do trades is to have a Bitcoin and to use portions of the Bitcoin to do the purchases. Correct?
Yes, but coins are just what we mention to talk about exchange of value. That value which is spent or that you own could be 0.0001 if you wanted (not that it's practical now). But yeah, it's true that you spent parts of your Bitcoin to do purchases, if you own just exactly one.
3. If I choose Bittrex as an exchange, after registering, I would transfer the Bitcoin from my wallet and deposit it into my Bittrex account. Once deposited I could use portions of my Bitcoin to pay for trading transactions.
Yes. I wouldn't call them transactions since they're not on the blockchain, but yes.
4. During the trading I will have to have a separate wallet for each type of coin I end up with? Or can I just store the coin in my Bittrex account?
Exchanges are not very safe. Cryptocurrencies have a terrible history with exchanges - one altcoin exchange called Cryptsy just vanished with all its users' funds and legal action against them is still in progress but people haven't got their coins back.
With regulation in the future this could change, but I wouldn't keep coins in the exchange for any longer than you absolutely need to for trading. If you see any bad signs or evident incompetence from the exchange, withdraw and switch. I see that you picked Bittrex first over Poloniex, good job.
5. If I decide to do some trading on Poloniex then I will have to withdraw what is left of my Bitcoin from Bittrex and deposit it into my Poloniex account.
Yep.
6. Are there any wallets that can hold multiple coins like Eth, Btc, LSK, etc?
There are wallets like
Jaxx which can allow you to store multiple coins while controlling your private keys. I don't know where it supports Lisk, but I wouldn't trust online wallets that support that many coins so I would personally feel safer going with Jaxx. If there's any coin that it doesn't support, just download their respective reference client (it shouldn't be hard to have a lightweight/SPV node for most coins).