I've had my bike inbetween 200 and 500 miles and I had my first two chain slips. Both of which happened when I was going down a steep gradient for the bike. I am thinking that it was most likely because I may not have kept constant tension on the chain causing it to "jump" off track. Is this the case or does it need to have the chain cleaned and lubed? Also how often do I need to clean and change lube on a fixie? I'm new to this type of stuff coming from a hybrid bike.

Your chain slipped and dropped?

Or is it your cog that slipped and you felt like you were "coasting" for a bit?

My chain completely came off.

Assuming it's the same thing that's happened to me recently, I'm going to guess it's a combination of your chainring not being perfectly centered/round and/or your pedal stroke not being completely smooth at the high cadence you were at. I suspect this combo results in the chain tension "pulsing" at the right amount & frequency to cause the chain to slip or drop.

Yea I cleaned my gears today and took off my fenders and it was impossible to take the chain off until taking off the tension of the back tire.

If you had had anywhere near the correct chain tension, neither of these would be a legitimate problem.

if your chain was too tight, it can cause chain to come off as well right?

no

If you had anywhere near the full details of my story, I'd consider your statement a legitimate comment.