The Sages enacted a prohibition against performing certain activities – such as bathing and haircutting – in the afternoon before reciting Minha, as one’s involvement in these activities may cause him to forget to recite Minha. Therefore, starting a half-hour before the time for Minha, one may not bathe or take a haircut until he recites Minha.
The Shulhan Aruch (Orah Haim 89:7) rules that this provision was not enacted with regard to Shaharit. Since it was not common for people to engage in these activities early in the morning, the Sages did not forbid them before reciting Shaharit in the morning. Therefore, if one awakens within a half-hour of Alot Ha’shahar (daybreak), he may bathe, shave and take a haircut, despite the fact that he is within a half-hour of the earliest time for Shaharit.
After Alot Ha’shahar, however, Halacha forbids performing one’s personal needs before tending to "Hefseh Shamayim" – "the needs of God," or prayer. As such, one should refrain from shaving before he recites Shaharit, unless he shaves before Alot Ha’shahar. There is, however, room for leniency if one shaves every day in the morning before Shaharit as part of his morning routine. Hacham Yishak Yosef, in his She’erit Yosef (vol. 2, p. 277), rules that if one shaves every day before Shaharit, we might perhaps view his shaving as grooming in preparation for prayer, in which case it qualifies as "Hefseh Shamayim." Therefore, one who normally shaves each morning before Shaharit may continue doing so, though Hacham Yishak writes that it is preferable to shave only after Shaharit.
As for showering, many people find that showering in the morning helps them feel refreshed and rejuvenated, thus enhancing their ability to concentrate during prayer. Such a person may certainly shower before Shaharit, as this would be considered part of his preparation for prayers and hence constitutes "Hefseh Shamayim." Otherwise, one should not shower before reciting Shaharit.
Those who have the custom to immerse in a Mikveh each morning may certainly immerse before reciting Shaharit, as immersion qualifies as "Hefseh Shamayim," rather than one’s personal needs.
Summary: One should not shave in the morning after daybreak until he recites Shaharit, though there is room to allow one who normally shaves every morning as part of his morning routine to shave before Shaharit. One should not shower before reciting Shaharit in the morning unless this helps him feel rejuvenated and will enhance his concentration. One may immerse in a Mikveh before Shaharit.
