No, I think you misunderstand, you cannot mine with Multibit, you need separate software for that, however I highly recommend you don't mine bitcoins on your computer. Multibit only keeps your private keys (aka your wallet).
I can explain some mining concepts for you here:
-----------
Cloud Mining - You buy Gh/s (mining power) from another company that owns a lot of mining hardware. They mine for you, and you get the money essentially. The Gh/s:es is also traded between the customers, which means you could end up selling your Gh/s for less than you bought it for.
-----
Pool Mining - You connect your mining device (Computer, ASIC, Phone) to mine together with many more people that does the same thing. The Pool gives you a specific task, and you get paid for each of these tasks you solve (if the pool solves the block first of course). Don't do this unless you have an ASIC.
-----
Solo mining - You let your mining device mine alone. It will try to solve the block itself. Don't go for this no matter what.
-----------
You could also mine Scrypt based coins, and in that case you could go for pool mining if you have a good GPU. You can then exchange the coins earned for BTC.
There's no need to use both MultiBit and Bitcoin Core, neither it is to have many separate addresses to get some dust from faucets.
Ok, I thought I had missed something huge, thank you for clearing a few things up for me. I'm not going to mine with my current computer, lol. Obviously it's a bad choice, but it finished syncing all the current block transactions to my external hard drive so I have that, and won't need to sync this far when I get started (probably a year, lol) down the road with the new computer. I don't know what ASIC is, so maybe I'll look into that, today.
Maybe I'll look into the hardware section to to see if there are any already posted builds people prefer for mining that are in my budget zone, and get info on that or whether my current build is good to go.
Thank you very much for all the help and info! Obviously I have a ways to go before I really get the ball rolling. haha
