It's impossible to tell if that rope is suitable for full suspension hanging or not, since we don't know what its safe working load is. I would suggest buying a new rope just to be safe... but if you can't, you could test out the rope you just showed us by hanging on it using your hands instead of your head.
It seems to me that the concept of "anchor point" isn't clear to you, so let me explain: an anchor point is basically something you tie your rope onto so that it holds your weight while you hang.
The beam you showed us seems like a good anchor point, so that means you can tie your rope to it and it should hold your weight while you're hanging.
I hope that clears it up.
By the way, you seem too nervous about this, are you sure you wanna do this? To me you don't sound ready. But hey, maybe I'm wrong in thinking that.