We pray for mashiah to come. After mashiah has arrived, are those prayers eliminated or changed? Also, will Halacha itself be changed or eliminated?
I don't recall seeing this particular issue addressed, although it may be explicit, but there is a very similar point made in Hilchos Birchas Hamazon.
The Tur in Orach Chaim siman 188 and explained in the Aruch Hashulchan there addresses the issue that Birchas Hamazon is of biblical origin, and yet we find a plea for the rebuilding of Jerusalem as well as a thanks for the land Hashem had given us. The explanation given is that there basic bracha is of biblical origin and the details are pending the situation. So originally they would say רחם על ישראל עמך but they would end off not by mentioning ירושלים but rather they ended במושיע ישראל. Same idea with ברחת הארץ they did not origionaly say על הארץ ועל המזון but rather מנחיל ארצות ועל המזון. Only after they captured the land did they say על הארץ ועל המזון. Likewise after King David captured Jerusalem he added ועל ירושלים, and after King Solomon built the temple he added ועל הבית הגדול. Along these lines they did not say ובנה ירושלים but rather ותמשך מלכותך, וחתמו במושיע ישראל. After the churban the nusach have was established.
It seems quite plausible that When Moshiach comes, all these versions will return to the state they were in during the time of the temple. Assuming so leads me to think that all the brachos in Shmoneh Esrei will undergo a similar change, where all requests for the future are turned to thanks for what we received.
This is all assuming that we will keep the basic format of Shmoneh Esrei introduced by the Anshei Kinesses Hagdola.
There is a dispute in the gemara Shabbos 151b, Nidda 61b:
מצות בּטלו לעתיד לבוא
Whether mitzvot will still be obligated in the future time of the resurrection of the dead. However Tosfos in Nidda prove that Mitzvos will still be binding. And theologically this is the mainstream belief.
However, there is a dispute if the Gemara should even interpreted as presented above (קובץ שיעורים (ח"ב סימן כ"ט)
This does have ramifications regarding the burial of the dead in shrouds that have Kilayim- forbidden mixture of wool and linen, for if there will be mitzvos when they wake they will find themselves wearing a forbidden mixture.
Thus, we see that there is a discussion in traditional Jewish sources whether or not mitzvos will apply on the messianic age.
see here for a fuller treatment (hebrew)