1. Do you have any problem?

2. Do you have any problems?
(Are both OK? Which one is popular?)

3. It is very cruel of him to kill a dog.
4. A dog is very cruel of him to kill.
5. He is very cruel to kill a dog.
6. How cruel of him to kill a dog!
7. How cruel he is to kill a dog?
(Which ones are correct? What about #4? Is #4 correct?)

1 and 2 are ok. 1 could also be "Do you have a problem?" (because it is only one)

#4 is quite awkward as a dog is not the subject, but the object. The rest are fine, but do y ou mean a question mark for #7?

Sra