(a) How can one betroth a woman with Mei Hatath? Does not all Mei Hatath belong to Hekdesh? After all, the Parah Aduma is purchased from "Terumath Halikshka"?
If someone wants to buy for himself some of the Mei Hatath - can the Gizbar sell it to him? Since it may only be used for the purpose of purification - what is the value of the purchase?
Perhaps it was the custom of the Hekdesh to sell the quantity needed for purification to the person needing purification - in which case this person can give the purchased quantity to a woman for betrothal and she can use it for her own purification, or for that of someone else, or she can sell it to someone needing purification?
(b) Kidushin 58B:
Rashi D'H Bischar Hava'ah explains that the Beraita saying one cannot betroth a woman with the act of Haza'ah is because "Schar limud mitsvah hu notel".
What does Rasi mean with the word "limud"? Wouldn't the phrase "Schar mitsvah hu notel" be better?
1) "Mei Chatas" refers to the water itself, as the Gemara implies when it says that one takes the money for filling it from the spring. "Efer" relates to the money paid for delivering the Efer from the Beis ha'Mikdash to the person who is Tamei.
2) The Mefarshim explain that for any Mitzvah which entails Tircha one may take payment, because it is not obligatory on any one in particular. However, one may not receive payment for a Mitzvah which does not entail Tircha, because it is like " Limud " about which it is said, "Mah Hu... Af Atah...."