Should vowed fast be offered in consecutive days, or not?

Vowed fast should be offered in line with what was originally intended by the vow-maker, either consecutively, or not.

Is it incumbent on a wife whose husband hasn`t gone to bed with her (for sexual intercourse) for many years to observe `Iddah (waiting period) upon his death?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhmmad and upon all of his family and companions.

Upon the death of the husband, a wife is obliged to observe the `Iddah even if he hadn`t slept with her because she inherits him. And Allah Knows Best.

What is the ruling on having brotherly ties between a strange man and a strange woman, and is the former considered a Mahram (unmarriageable) to the latter?

Such a relation between a strange man and a strange woman is forbidden in Islam because it involves forbidding what Allah has allowed by marriage, and allowing what Allah has forbidden such as looking and the like. Such a relation doesn`t render any act lawful between them, thus they are forbidden to look at each other, have a Khulwah (seclusion), and travel together.

Is Zakah (obligatory charity) due on land intended for selling?

Yes, lands intended for selling are evaluated, and Zakah is paid according to their estimated value after a lunar year had lapsed, but if the owner didn`t pay the due Zakah, then he should do so after selling them.