It is forbidden to pray or recite Berachot in a public bathhouse, such as a Mikveh. This applies not only in the interior area of the Mikveh, where people actually immerse, but even in the changing area. Although one is allowed to silently think about Torah matters in the outer chamber, reciting words of Torah, Berachot or prayers is forbidden. (In the inner chamber, it is forbidden even to silently think words of Torah, even if nobody is present.) Therefore, one who wishes to eat or drink in the Mikveh – even in the changing area – may not do so, since he may not recite a Beracha.
For this reason, a water fountain should not be installed in a Mikveh, as drinking is not allowed.
Some Poskim allow reciting a Beracha over some water or food before entering the Mikveh and then eating or drinking there, with the intention that the Beracha should cover also what he wishes to eat and drink inside the Mikveh. One may rely on this leniency when necessary.
In the inner area of the Mikveh, one may not greet his fellow with the word "Shalom," as this is considered a Name of G-d. If, however, someone is named "Shalom," it is permissible to call him by his name, since "Shalom" is then being said as a reference to the individual, and not to the Almighty. (By the same token, if somebody named "Shalom" wears a piece of jewelry with his name, he is allowed to enter the restroom with it.)
One may recite Berachot or even pray or recite Tehillim in the area of the Arizal's Mikveh in Tzefat, as long as nobody unclothed can be seen. The Arizal's Mikveh differs from ordinary Mikvaot in that it is not heated at all, and the water remains cold. An ordinary Mikveh is considered a place of filth due to the steam, and so the Arizal's Mikveh does not have this status. This applies to any cold pool, even if it is used as a Mikveh.
After immersing, one is required to wash his hands. For this washing, it suffices to wash each hand once.
Although one should not store food in a restroom, it is permissible to store food in a Mikveh.