Exactly. Priests were shipped over. And so were agents, not ordained, of the Bishop of London, to watch over affairs. Confirmation was limited to episcopal visits or required returning to the mother country, where the episcopal hands were located. Hence the phrase, still in the BCP (1928, at least; haven’t looked in the '79), limiting communion to those confirmed or desirous of being confirmed. A recognition of the situation.
Yes. The CoE was the established Church in a number of the colonies. Five, to my memory; I’m too busy/lazy to seek the info out. And there was no problem with the points you raise, when the colonies who made the CoE the established Church did so, in the early 1700s. It was the CoE, and the CoE met all the conditions you mention.
OTOH, since (IIRC), other colonies had established Churches not being CoE, the requirements you listed were not mandatory. The establishment lingered on, theoretically, in state constitutions, until well into the 1800s.
GKC