"Once I eat what looked like a giant circle and it ended up dividing me into smaller circles"
That's a virus. :) If you are bigger than that, it divides you, if you are smaller, you can go through it safely.

"since all I do is move my mouse around."
Actually, you can half yourself with the space button. That's how you can jump on and eat smaller players, or run from bigger players (because the smaller blobs are faster). But you have to be careful with it because for a few seconds you can't unite the smaller pieces, so even a smaller cell can eat you if he is bigger than those small pieces of yours.
You can experiment with the W button too, it can be helpful in some situations (I don't use it too many times), you divide yourself with that to smaller pieces too, but without the jump.
Another advice is to use F11 at the beginning to play Full Screen. Good luck! :)