Creative and cooking processes take time. Where nothing really appears to be happening. Ideas become richer with time.
Acceptation helps: you won't feel like sh anymore. Acceptation also means "let's go for a walk" is often your best option.
A todo list, the pomodoro technique (google it), relaxation/meditation can help too.
Productive procrastination is also a good way to cope: find a better procrastination, learn something, anything that will make you a better you...
So yes, I account for procrastination in time estimates. I think "nobody" can be 100% productive for 8h a day for some jobs.
EDIT: by definition, time estimate means "how long will I take to achieve X", so including procrastination in it sounds right...
When you ask if you are normal, you at the same time define "not normal" and put yourself in that box, what about rejecting the concept of normal and work on accepting who you are?
On the other hand I understand and recognize what you describe, sounds like what I used to do and what I have seen in many.
Try this: Divide your project into timeblocks of half a day's work (not in hours but in a size you can realistic reach either before midday or from midday until end og working day)
Then take a piece of paper and make a grid with the five weekdays and two cell's per day and write one of the timeblock you defined above in each cell.
Then show someone this paper and hang it somewhere visible, this is your accountability.
Then in each timeblock, after reaching your task, mark it complete and procrastinate until the next timeblock begins :)
This helped me.
Edit: then only sell timeblocks not hours - that way you get paid for doing tasks not doing hours.