If one needs to daven shacharis at a super-early (i.e., post-dawn but pre-sunrise) minyan, what is the correct procedure for putting on Tallis and Tefillin? At what point are they put on, and which berachos/pesukim are recited?
I have been having this experience for a while. Before answering any of the above, be advised that my Rav paskened for me that if I have time to daven later individually, I should not daven with a minyan that says birchos krias shema/shema before misheyakir.
Talis can be put on at any time with the bracha said after misheyakir (This is the general custom acc. with the GRA- Shulchan Aruch O.C. 18:3; M.B. 10) We don't interupt pesukei d'zimra for this bracha (S.A.-O.C 53:3), but you can say the bracha between yishtabach and kadish (but, surprisingly, not between kadish and barchu!) (Rema S.A. O.C. 54:2) If you accidentally said the beracha early, you don't repeat it and rely on those who say night is included for tzitzis (night beged is excluded).
Tefilin is a big debate. The consensus is that you can put the tefilin on if you must get up early to go somewhere. Acc. to those who say it's not time for tefilin, you just don't have a mitzva until misheyakir. Acc. to those who say that Chazal forbade it because of a suspicion that the wearer would fall asleep, this case Chazal allowed because the reasoning didn't apply.
The debate comes on the bracha: One shittah (Rabbeinu Peretz) apparently holds of the 2nd approach above- it's time for tefilin and Chazal permitted putting them on early, so you can make a bracha. This is the "official minhag" in my minyan (they only announce talis after misheyakir).
Most poskim (Shulchan Aruch 30:3; Aruch haShulchan 30:5; et al.) I have seen say to make a bracha after misheyakir. (See procedure for Talis) (Mishna Berura 53:6; Aruch haShulchan 53:2- though I have seen sources for making the bracha between paragraphs of pesukei dezimra). If you made the bracha too early, you can rely on the previous shittah and do not repeat it.
The custom is to make some minor usage of the talis (Shulchan Aruch O.C 18:3) and tefilin (30:3) before the bracha (memashmesh)