There are many plausible ways to see the chords, and all of the interpretations are equally true at the same time.
- Eb9#11 : can be used like you would use (1) Bbm (or Bbmmaj7) in the key of F major, or (2) tritone substitute dominant A7 going to Dm, or (3) F7 or Cm going to Bb major, ... or maybe (4) like an Eb7 or Eb9 if this was a mixolydian blues/funk/soul thing in F.
- Bm7b5, a.k.a. Dm6/B (it has a Dm in it!) : this kind of "resolves" the Eb9#11 to a Dm which was one of the possible expectations or interpretations above, but it's not just a regular Dm, there's an additional twist, the B in the bass. A nice and easy thing after that would be Bbm6, feeling like a quick release to tonic F. If not even blatant F/C - C7 - F. But that's not what you get, things move slightly to the minor side with a chromatically descending bass line, Bbm7 - Am7 - Abm7 - Gm7 ... so a quick release ii-V-I cannot be far away anymore?
As a dominant there's a Bbm6/C, which sounds like a variation of the Eb9#11, it's just a notch closer to a plain vanilla C7.
IMO it's best to analyze jazzy chords in terms of a set of things you can do with the chord, and not try to come up with "it is a ... blah blah chord" sentences. The "is" sentences just don't cut it. Each chord is what it is, many different things but none.
Try to use the chords in the various roles. For example the Eb9#11 could work in place of a dominant C7 in "Happy Birthday" in F. "Plagal cadence" ... sort of, I guess? Try the alternative expected resolutions for the chords. Dm and Bb work after the Eb9#11, don't you think. How about after the Bm7-5... C/Bb - F/A - Gbdim7 - Gm7 - C7 - F. Or how about Bm7-5 - E7 - A7?
Or to try interpretation (3) of Eb9#11: whenever you have a regular F7 - Bb chord progression, try replacing the F7 with Eb9#11.
To "understand" chords like that means, in my opinion, that you can see the possible different interpretations at the same time, and you can use the chords in the different roles in different contexts. It's like with borrowed chords - you have to see the other parallel interpretation from which you borrow. And you have to see the Dm in the Bm7b5, otherwise you don't understand the chord. Chord symbols are just a shorthand notation for groups of notes. The written root note of the chord symbol doesn't necessarily have to be the be-all-end-all definition of functionality like it's in simple traditional functional analysis, because there are multiple plausible functional stories in parallel. In "Bm7b5", sometimes the "b5" can be the most important note.