Is it normal to get fluid pockets under your eyes right after eyelid surgery?

Yes. After yeylid surgery, specially the lower lid surgery it is common to have pockets of fluid under the eyes. Keeping your head elevated , specially when sleeping, can help a lot. Using warm compresses 2 or 3 times daily also helps. Typically after few days to weeks they all disappear.
Yes common. Yes this is quite common. It hey are typically worst in the morning and may be minimized with gentle compression, elevation, ice compresses. The use of manual lymphatic drainage may help but should be discussed with your surgeon.
Yes. It is very common. Often md will suggest head elevation and moist, warm packs be applied for the first several days to weeks to assist in reduction of the fluid. Time typically corrects all such "pockets" as healing progresses.
Yes. Immediately after surgery it is not uncommon to have some swelling and perhaps some fluid collections under the eyes. This usually resolves over a few days.