I agree on both points... try to avoid yanking old leaves from aloes unless they give easily. A pair of scissors should do the trick. These plants grow a bit of a stem as they age and it's nothing to be concerned about.
Do not bury the stem on an aloe (or most succulents for that matter) because that will almost certainly trigger rot.
That's a pretty small pot for the size of the plant. I would think you could double the width of the pot, or at least go one size up for starters when you repot, and the plant will be fuller and more prolific as a result.
