tefilla - The origins of davening

So according to the Rambam (I believe that it is only him, but would be more than interested in other people that also hold the same view), it is a mitzvah de'oraita daven every day (I believe its one thing each of shevach (praise), hoda'ah (thanks) and bakasha (petition)).

Today we fulfill this thorough the shmoneh esri, and the structure matches (first three, middle, last three) and all is good.

My question is threefold:

1 . What were communal prayer like in the times of beit hamikdash? It would seem from the gemara in Megilla 25b that there was some form of prayer going on whenever their ma'amad was up in the beit hamikdash, but rashi over there says that the town square does not get kedusha from this as it was not set/regular enough (seemingly, this was only done for two weeks a year and when there was no rain). It would seem odd if there was no daily communal prayer though as there was a beit keneset (though I suppose that could be for monday, thursday, shabbat, etc)

2 . Was there prayer two or three times a day? (I would expect that Ma'ariv is a probably not, as that was accepted as a minhag later I think)

3 . In a gemara in brachot (sorry I can't seem to find it), it would seem by juxtaposition that the korbanot and the daily prayers are related at least in their times. Did the three daily prayers come from the two daily korbanot and the trumat hadeshen?

Of course, if we don't hold like the Rambam, and say that prayer is rabbinic, do we say that there was any kind of prayer other than when an individual felt like it in the times of the beit hamikdash?

EDIT: here I am using times of the beit hamikdash to refer to beit reshon, as in the times of biet sheni there was the shemoneh esri already. It would be interesting to find out the "rollout" as it were of the shmoneh esri and start of reading the torah on monday tuesday and thursday and how they came about, but that is for another question I think.

Answer

Before the anshei kneseth hagedolah created specific formulations for prayers and blessings, people recited it how they wanted. They would pray to G-d frequently, not just when it was their turn to ma'amdos. As for communal prayer, it may be they did not have set times to daven together. However, they did gather to hear the Torah on shabbath, and Ezra institutes that it also be read on Mondays and Thursdays.

Before the churban bayis rishon, people did not necessarily pray 3 times a day. This was instituted after the destruction to correspond to the 2 Tamid korbanos (shacharit and mincha), and to the burning of the leftovers from the korbanos (hekter chalavim v'evarim). Because this was not necessary if there were no leftovers, Ma'ariv does not have the same obligatory status as the other 2 prayers.

(Although the gemara also mentions an opinion that the tefilloth also correspond to the Avoth, they still correspond to the korbanoth.)