A: yes.Cleaning very well is always a must.When i bought this product 5 years ago, it said in the instructions that there is no sanding required.It also said that you could use it on laminated cabinets. I put on three coats with a smooth small roller. It has been over 5 years and still looks great.
A: Just clean and rinse very well.If there is any existing scratches or abrasions in wood,than you would want to lightly sand.But product adheres very well with proper drying time and 3 coats.Most latex based paints will dry to the touch very fast, but will take a good month to completely cure.
A: Previous commenter Julie has it right: cleaning is essential. But if you use TSP, take care to get any residue off, as it will lead to problems with most modern paints. I would add scuff sanding with 220 sandpaper and possibly a thin coat of Stix primer.
A: Did you degrease your doors and drawer fronts? If so, did you use a cleaner like TSP after degreaser? I would sand then reapply the paint.