Do I need to tape drywall behind cabinets?

Answer: Yes
Explanation: Whether surface is finished (ie: painted or primed), my recommendation would always be a surface sealed as much as possible to prevent future issues, such as mold. Taped and mudded joints and seams will help prevent future - and costly- issues.

Answer: No
Explanation: However damaged drywall must be repaired with new drywall material prior to backsplash installation.

Answer: Yes
Explanation: depending on how the cabinet style is.

Answer: Yes
Explanation: This is preferred but mostly for esthetics reason for future remodel possabilities.

Answer: No
Explanation: I would unless it required

Answer: Yes
Explanation: All construction installs must be completed