Regarding the source of wearing special clothes for Tefillah, the Pasuk of "Hichon Likrat Elokecha Yisroel" from Amos is quoted. I find this a little inauspicious, because in context the Pasuk has very negative connotations - prepare to do battle against Hash-m.
Good question. However, the only commentary who says that the verse means "prepare to do battle with Hash-m" is the Metzudas David.
Rashi, the Radak, the Targum, and others explain that it means, "Prepare to do Teshuvah and good deeds," which includes prayer.
According to the Metzudas David, however, your question remains. (See Maharsha in Berachos (23a), who says the words "Hikon li'Kras" mean prayer.)