Hey buddy, welcome to crypto.
I have no favorite online wallet (see answer to Q. 1).
nicehash is good mining software (user friendly, easy to use as you don't need to care converting mined coins to BTC ). Definitely recommended for newbies.
The only online mining companies I trust are: hashnest, bixin and BW. ( all others are just scam or very close to scam .. try to avoid them)
Why those three? Because they are big players in this industry, running for long time.
NOTE: You will not earn much just from the mining. You need to constantly buy/sell hashes to make some profit (this is case of hashnest, bixin ... BW offers only contracts)
1: Whats the difference between Online wallets and Wallet software (I dont know how to explain this,but I know that there are some softwares that you download that weighht like 110GB and act as your wallet)
Most online wallets will not provide you with privatekeys (which is the key to bitcoins held by address) .. this means you have just their IOU promise.
2: What is Bitcoin Core?
Basic (original) software (GUI) used to communicate with bitcoin network.
3: Now Im rocking "NiceHash Miner 2.0.1.1 Beta" as miner and "blockchain.info" as wallet. Is this good set-up?
Yea, nothing against.
4: I know this may sound very very very stupid but do this actually work? It seems too good to be true to earn 2 USD a day by just IDLEing my PC (
http://prntscr.com/gi1y63) (and yes, I am aware of the electricity bill).
It's not idleing. Your GPU actually works pretty hard and wears off.