Thanks for everyone's help so far. I removed the pump from the machine tonight and I guess I don't know enough about vibration pump to know if there's anything wrong with it. All gaskets and the seal at the metal cylinder still look pretty good. I am bit confused with what I saw on the intake part which I will describe below.

Here's the complete Fluid O Tech pump sans the metal plate screws and nuts (Edit: and rubber band):


Here's the intake side of the pump:


Here's the outlet side of the pump (Edit: do I have the sequence correct? I forgot to take pictures of the outlet side to show how all the bits go together):


Here's what I don't understand:


The large spring on the intake side has a plastic tube that, itself, holds a much smaller and thin spring inside. In order to secure the small spring and the tube to the large spring, FOT used some kind of whitish/grayish glue and made quite a mess. As I look straight down into the white tube, I see that the glue covers the entire tube opening. I used a pin to prick a tiny hole in the glue to verify that there wasn't any opening before. The glue also overflows and covers the flange of the white tube, but not completely. I am thinking that due to the incomplete glue coverage in this part, the pump is able to pump in water and the water, instead of passing through the tube, passes on the side of the flange where there is no glue. Since the opening as the flange is pushed against the housing is probably smaller than needed, the pump can only suck in so much water. Maybe this is why I saw the low flow that I posted in the first post.

After writing all this, I just remember that when I first removed the plumbing at the pump's outlet, I tested the pump for a few seconds and it seemed to be able to pump a good amount of water. Unfortunately, I didn't capture the water to see if the flow rate with no resistance is normal.

If you have opened up the FOT pump before, do you remember seeing something similar or is there a hole for the water to pass through to the inside of the spring?

Thanks for reading all the way to the end. I tend to be a bit wordy.