Hiya Keven. :)
I will address your questions in order :
1) The fact that the floating bridge has gap(s) at it's edges - where it does not follow the arched contour of the guitar, is a common problem ; remedied by trying one of the following two 'tricks'. It is not string gauge dependent.
Firstly ( and the simplest solution ) is to get a replacement bridge ( base ) that has a gap in the centre of it's base. This allows it to readily bend / follow the contour, without sanding. This is my usual solution, if the wood of the stock bridge is too stiff to 'flex'.

This second picture shows the type that you may have and I have had - that often needs shaping to the guitar top. You need to carefully hold sandpaper ( grit side up ! :lol: ) on the guitar top, and sand the bridge against this to fit.
2) You can use ( as I do on mine ) 14 - 55 gauge strings in standard tuning, no problem, as long as you set the truss rod accordingly. This is further assured by the fact you have a 'Lyre' type tailpiece - which makes heavier strings feel lighter. I would however, recommend Thomastik-Infeld 14-55 'Be-Bop' strings, not just for tone, but because T.I. strings have a relatively lighter gauge on the bottom four strings, than any other type - all without loss of balance or volume. They also have round core bass strings, which are more supple. The overall effect is that the fretting hand feels very comfortable, even with a Barre chord on the higher frets e.t.c.
3) Set the truss rod appropriately , and use it with the strings heavy and low - otherwise , you might as well pick up any 'ordinary' guitar , if you want lighter gauges and string bending. I do not recommend using a Jazzer just for 'Fancy Dress' purposes. For a Jazzer to feel comfy, take advantage of the heavier string's ability to remain rattle free and 'in place' at an action of about 0.7 mm ( 1/32" ) at the 12th fret.
I have even strung my Les Paul with T.I. 14-55s with no 'accidents' , but the standard tailpiece - and mechanics thereof, make it feel much stiffer than a Lyre tailpiece.
4) the 25.5 " scale you have is going to feel stiffer anyway, as the ideal scale for a 'softer touch' is 24.75". As a result, you might want to start at T.I. 12 - 50s (?) - the main point being that T.I. ( and to a lesser degree Newtone Archtop strings ) - with their relatively heavy bass strings ) are designed to break in and sag better under your fingers. Try the same gauges in conventional 'Rock/ Blues' type string brands, and they feel like fence wire !
5) As for the T.O.M bridge option ; buy it as an experimental spare ( I have a couple of each type in my parts box ) - but there is no real advantage over wood, and in fact most ( including me ! ) prefer the wooden bridge option, for tone and feel. The T.O.M. bridge top option only became fashionable, to placate the players who did not want to set the intonation on an archtop the 'old fashioned way' by shuffling the entire wooden floating bridge around , till it was spot on. I actually find a fully wooded bridge a lot faster to intonate than a T.O.M.
As for the tonal attributes of T.O.M. bridge tops over wood ; we all have our preferences - but to over generalise somewhat - wooden bridges seem to subtly blend the notes together a bit, and dampen harmonics /
initial sustain a touch. However , this gives rise to a note with strong fundamentals - and a sustain that 'blooms' up
after the note begins to sound. Both of those qualities are 'Jazz desirable'. There is no right and wrong, but for me, an all wood bridge sweetens a bright guitar, and the metal topped T.O.M seems to add a little punch to the notes on a darker sounding guitar.
Finally ( for now ) - do not get too hung up on it's acoustic sound, as the amp can be quickly E.Q's to match the guitar. Yes, a nice acoustic sounding guitar is a hint of great things to come, but bear in mind that even elite guitar builders like Sadowsky / D'Aquisto e.t.c, often use laminate guitar bodies, as that often gives a sweet amplified sound, if you want the darker, Grant Green, Wes Montgomery type tones. A fully carved solid wood guitar is most desirable of course, but is not always 'King Of The Hill' when amplified. Different, but not always better.
I hope that gets you started . :)