Is it possible to complete all the side quests in a single 3 day period?

Solution 1:

This is impossible. For a start, to win the lottery side-quest you have to go back in time at least once to know what the numbers are going to be/were.

To get the lover's mask side-quest completed you need to return to the first day and show the lover's mask to the major to get a heart piece.

Solution 2:

To answer the original question and the edit at the same time:

No, it is impossible.

To get the All-Night mask at the Curiosity Shop, you must save the old lady in North Clock Town on the first night. This causes Sakon not to visit the Curiosity Shop, stopping the Kafei-Anju quest, meaning you cannot get the Keaton mask, or the Lover's mask.

Solution 3:

No.

This walk through of the Kafei and Anju side-quest states it can be completed in two different ways, one of which gives a bottle, the other the postmans hat:

Remember that letter that the Curiosity Shop man gave to you? Well, it needs to be delivered to Madame Aroma. You can either hand deliver the letter to Aroma (you’ll need the Romani Mask for this), or you can hand the letter to the frantic postman at the post office. If you choose to deliver the letter to Aroma yourself, [...] she’ll reward you with a new bottle that’s full of Chateau Romani. If you take the other route and give the letter to the postman, [...] talk to him to receive the postman’s hat.

There are a few other sources stating the same thing.