Can someone who begins a voluntary fast break it?

What is the ruling on a suitor (khāṭib) going out alone with his fiancée before the marriage contract is concluded?

It is unlawful for a suitor, prior to the marriage contract , to do anything that would be unlawful for any non-maḥram man — including touching his fiancée, being secluded with her (khalwah), or seeing her without her complete sharī‘ah-compliant covering — even after the recitation of al-Fātiḥah (This is a cultural custom to seek Allah's blessing (barakah) and mark mutual consent) and the family's approval [of the engagement]. This is because the engagement, without the formal marriage contract, does not render unlawful matters permissible. And Allah, the Exalted, 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.

What is the ruling on performing dry ablution (tayammum) instead of the ritual bath due to severe cold?

Whoever is sick such that he cannot use water, or finds the water cold and heating it is not possible, and the person would be harmed by using cold water, it is permissible for him to perform tayammum. He must make up what he prayed with tayammum, because this is a place where there is water. And Allah the Almighty knows best.