Free and Safe Video and Audio Recording Software for Mac?

I'm starting a new YouTube channel today (Microbiotic Gaming if you feel like checking it out) and I was wondering if there was any free sort of Fraps recording software (not actually Fraps because that would be illegal). What I'm looking for in this software is as follows:
A) It can record the screen of my computer and in-game sound effects
B) It can record background audio (my commentary)
C) It is safe and not just a copy of something else or something that's 'free' (e.g. "Free" Fraps)
D) It is legal to download
E) It doesn't lag my computer significantly enough (it would be awesome if it was lag-free) to impact gameplay/computer functions (I have a MacBook Air with a 1.7 GHz Intel Core i5 Processor, 4 GB 1600 MHz DDR3 Memory, and an Intel HD Graphics 4000 1024 MB Graphics Card)
F) It's free (LOL)
Also, a link to a safe place to download it would be nice, but if you don't know a website/URL, that's fine.
Thank you so much for your help and answers.
Cheers,
David

Added (1). ***THIS IS INFO ABOUT MY CHANNEL, IT IS NOT IMPORTANT TO THE QUESTION***
If you do want to check out my channel, just keep in mind it is brand new, and it most likely won't have anything up until I find a good recording software (hence me asking this question). If you could subscribe and give me feedback, that would be awesome. Also, a like or dislike would be great too (dislikes help me learn what you guys don't want uploaded)

Added (2). I found a way to record video and audio, but is there any way to synchronize them together? Is there a safe, legal application that does it? Or do I have to do it manually

I'm PCs User, I crack bandicam full.
In Mac I'm not sure, you can use QuickTime To record it's free.
But you can't record your voice,
Use your IPhone to act it…
Pain in the ***, buy it…
You've no chances.
Edit,
Fraps has 30 seconds recording,
Still Pains.
You need to record every 30 seconds and make it together or mixed it.
Trusted me, it won't work.
It's hard.

There are not many free software's out there that actually offer you a full time deal, and does not lag your computer. I use Dxtory, it works perfectly for me. For audio I use Audacity. Not really sure if these are macbook compatible, but it doesn't hurt to try.

You may refer to this website, it's a list of the Top 5 free audio recorder for Mac. I personally like the Audacity.

http://www.mac-dvd.com/freeware/top-5-free-audio-recorder-for-mac.html

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