I was on estrogen but can't remember when they stopped it. I know I was on progesterone for 12 weeks after transfer.
i was on estrogen (along with progesterone) post transfer.
they will monitor you and have you stop the estrogen if you become pregnant.
I can't answer your question about what estrogen should be on the day of transfer but I am preparing for my FET now and am on estrogen tablets to prepare my lining which will continue for 17 days after the transfer. It is quite common to do an assisted FET as opposed to a natural cycle (just depends on your clinic) and very common to give estrogen tabs so wouldn't be worried about taking them.
good luck with getting your BFP