Well you are undetectable, so probably not.
Also opponents are 'frozen' implying they cannot take action.
In addition you cannot directly interact with anyone while under the spell so implicitly the reverse is true.
Given that "While the time stop is in effect, other creatures are invulnerable to your attacks and spells; you cannot target such creatures with any attack or spell.", then the caster should also be immune to attacks (more specifically, no attacks can happen vs the caster) during the time of the extra rounds.
I would say that "free to act" means no possible repercussions from their actions happen during the free rounds. At the same time, they don't "queue up" and occur when time reverts to normal for the caster as well.
No, you cannot take attacks of opportunity while you are unable to act.
Other creatures can't act during your time stop, and you can't act directly against other creatures. If other creatures can't act, they don't get to make AoO either.