1. They could just turn into the clear sleeves of the base item. Not exactly much.
2. They probably just fall out. But, there's no reason for something to not have pockets. Just put them on the inside if you don't want them seen.
Two questions about this item.
1) Can it transform clothing into no clothing? If not, what's the smallest, hardest to notice "clothing" it can turn into? Something like a small piercing? I want to pass off as having no clothes but be able to suddenly have them for disguise/sneak purposes.
2) What happens to items in a pocket of a coat, for example, if you transform it into another coat that has no pockets? Can you still access them... somehow? Or do they go to some magic place until it transforms back?
The "transformation" is only an illusion. Your clothes are still the same. Oh sure it says "Many Garments", but the item is lie. As seen here:
Sleeves of Many Garments: Are the effects of sleeves of many garments illusion or transmutation?
The effects are illusion (glamer) like the glamered weapon and armor properties. This means they can’t be disbelieved like a figment could, but they do not actually physically change the clothes. The transformation changes only the appearance, including the feel, smell, and other sensory aspects.
So the answer to 2 is you always have the pockets there. As to 1, I suppose whatever the smallest amount of non-magical clothing you can find is.
Ask your Dungeon Master.
If I were the Dungeon Master I would say choose from the list of clothing on page 159 (Table 6-9: Goods and Services).
As for pockets, I would abstract and say all of your items are available, use your imagination. If you can't imagine it--then you need pockets. Furthermore, this only affects your clothes. Your backpack, your armor, your weapons, headbands, goggles, masks, etc. etc. Are not transformed.