Is it permissible for a person who broke fasting in Ramadan because of being sick to pay a ransom?

If there is hope for him/her to be cured, then he would be required to make up for the missed fasting days when he/she recovers, and no ransom is due on him/her. If his/her disease is incurable, then he/she would be required to pay a ransom for each missed fasting day, which is (600) grams of wheat, or rice. And Allah Knows Best.

What is the ruling on shaving one`s beard?

All Perefct Praise is due to Allah The Lord of The Worlds.

Growing a beard is mandatory and must be abided by except for a sound reason. And Allah Knows Best.

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.

Should one fulfill his vow of donating an animal to the poor and needy with one sheep although he had repeated the vow several times?

Each vow has to be fulfilled, and repeating the words of the same vow for confirmation renders its fulfillment obligatory as one vow. As for multiple vows, they have to be fulfilled as well.