Maybe to the point where they take well established stuff and then render it unusable because of 'reasons' (that don't make any sense whatsoever).
Yes, but given how small the Federation became (35 or 38 planets down from 350 at its peak), its unlikely any of those are extra-galactic. They are likely INSIDE the Milky Way - and given what Vance mentioned about the Emerald Chain and limits on how few ships SF has right now, its very unlikely any of the planets are in nearby galaxies (though it WOULD be nice if they were).
My point exactly, but its very likely that the state of Warp technology is (probably) not that much different compared to the 24th century (given what we've seen thus far).
If they managed to double the top speeds every century (like they did from the 23rd to the 24th), and speeds increasing exponentially with every increment after 9.9, then that might be a rough equivalent of about Warp 9.97 (810 years from 24th century to the 32nd... minus 100-120 years if you factor in that technology didn't really advance/change since the Burn occurred [which is stupid enough] - resulting in about 700 odd years of advancement and twice the increase in speed per 100 years giving us something like this:
Warp 9.9 (21 473 times Light Speed) in late 24th century
9.91 (42 946 x LS) in late 25th century
9.92 (85 892 x LS) in late 26th century
9.93 (171 784 x LS) in late 27th century
9.94 (343,568 x LS) in late 28th century
9.95 (687 136 x LS) in late 29th century
9.96 (1 374 272 x LS) in late 30th century
9.97 (2 748 544 x LS) in late 31st century (this is roughly when the Burn happens too, so we should likely assume that no progression occurred since then (given how the writers apparently LOVE to do this) - despite the fact that technology would NOT stop advancing even after the Burn... if anything, SF has more than enough resources and supercomputers with every ship docked at HQ to continue making significant breakthroughs at faster than exponential pace... even with 38 planets remaining in the Federation and delayed subspace communications... but they probably won't even go down this route.
Not quite.
Burnham mentioned about 50% chance of surviving a passage through a TW conduit (which I think is ridiculous because SF had 810 freaking years to analyze and adapt to the stresses inside a TW conduit... and we know that when Voyager used a TW coil to open its own conduit along with the Delta Flyer, their structural integrities were perfectly fine - and that was already in the late 24th century).
Plus, SF no longer uses Duranium or Tritanium... they have a combo of Neutronium, holographics and organics... stuff that's arguably MORE advanced than what the Borg even used (their ships were Tritanium based much like Federation ships of the time).
As I said, the writers are taking well known stuff and just barely inching things forward (as if merely a few decades passed since the late 24th century... not 8 centuries).