What should one who made an intention, at night, to make up for a missed fasting day, but broke his fast on the next day?

One who started making up a missed fasting day, then broke his/her fast without a legitimate reason is considered sinful, and is only obliged to make up for the missed fasting days. And Allah Knows Best.

I`m infatuated with a man, is it permissible for me to make supplication that he falls in love with me and becomes my husband?

Islam has honored women by being proposed to by men, and not the other way around, so it is inappropriate for a woman to propose to a man since one who hastens in asking for a thing prematurely shall be punished by deprivation. In fact, such a phenomenon is the result of unlawful mixing between the two sexes.

Is keeping money in and taking profits from the Islamic Bank lawful? 

If Allah Wills this is lawful, because they stipulate on theselves to work in accordance to the guidlines of Islamic Law. And Alalh Knows Best.

A man donated a burial plot, but before registering it in favor of the Ministry of Awqaf and before burying anybody there he said that he didn`t want to donate it and planted it. What is the ruling of Sharia on this?

All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

If he had endowed it as a cemetery, then he can`t take it back, even if he didn`t register it in favor of the Ministry of Awqaf. If he said: "I have endowed this plot as a cemetery, then it becomes an endowment." However, if he didn`t endow that plot-but it was his intention to do so-then he is allowed to back down. And Allah The Almighty Knows Best.