Hi daejiny,
Yes, the clangy piano does not assist you much in this recording. It needs work, and not just tuning!

No, you don't exhibit any rhythmic problem. Some pianists do fall into the trap of playing this prelude in 3/8, but you correctly execute it in 2/8 as written. And your quintuplets are fine. You "push through" them in the stretto section very nicely to create a surge there.
I believe there are three other performance necessities in this brief piece: 1) Always play the long line (and you're on the right track there). 2) As to technique, always roll the left hand bass upward toward the objective with the right taking over totally seamlessly.
I listened again tonight, and believe the "bumps" I hear occur for three reasons: 1) When the right hand plays the second beat in a measure, it is always executing double notes. What's required there is to voice the top notes only while very much deemphasizing the bottom notes. 2) Also, the second beat in 2/8 is, of course, a weaker beat, so must be played with less emphasis than the downbeat. And: 3) The last 16th note in any measure played by the right hand ends a phrase, so there must be a noticeable tapered, lilting lift-off with the forearm and wrist, resulting in that last note being gently softer than the earlier part of the phrase. (Same with the left hand phrase endings as well.) Often you play those 16ths almost marcato such that there is little differentiation volume-wise between those last 16ths and what preceded them. Makes it sound a little boisterous. The punching of those notes contributes to the bumps.
So, I believe that if you could play the second beat as more of a less-pronounced weaker beat while, voicing the tops of the double notes more, and then gently taper off the quieter final 16ths in those measures, the flow will become more fluid, seamless and pleasant. And you'll like the additional clarity in your playing.
Just my opinion. I hope this helps.