This got long so I put it under a cut. A paragraph for each question.

Rupture’s favourite food wouldn’t be anything as gross as their twins gross watermelon concoction, I can imagine they’re into things a bit more mundane albeit probably have a small taste for blood/fresh Energon on account of probably absent-mindedly licking some off their fingers while feeding the Leeches.
Though I suppose they’d always have a soft spot for the home baked stuff, so probably one of Galvatron’s cakes would be their favourite. Though even then it’d likely be more on the plain side of things so just a slice of vanilla sponge.

Paradrox has a habit of stealing signs with preference to “Do not disturb” ones. It’s both something they do to decorate their living quarters and occasionally to indulge a little in the chaos the lack of signs brings. Though they do have hobbies that take after their creators a bit more. They’d like fiddling with things and building tiny contraptions like Galvatron, but also go for runs and general exercise to ‘keep on their toes’ like Cyclonus does.

Nipper, like Earth leeches, does not particularly need to be fed that often and really just needs a tank of water to keep clean and moist in and food. That’s it. Rupture just spoils them a bit and gives them a liiiiittle too much food and lets them perch on their shoulders. The more impressive thing is how Rupture managed to train the little bugger.
((You can actually keep leeches as pets! See this post for details! (contains blood, duh) fascinating stuff!)

Anywhere aesthetically pleasing. Rupture would want to go somewhere with a good view they can ‘indulge’ in and Paradrox is fine with travelling just about anywhere, if it’s ‘boring’ they can always make it not so.

Yes he does. All the time.
All of them have been on at least one ghost hunt with him.
Paradrox isn’t the best though as they’ll get bored easily, fidget and maybe mess with stuff they’re not meant to. Rupture has zero interest in it but can barely deny their baby bro much. Galvonus always accompanies him on every one because he has to protect his twin (He also does not trust this “Starshine” fellow Cyclotron has mentioned before). Bedlam is both good and bad on a ghost hunt, the bad thing is they’re messy and tend to destroy things, the good thing is they’re a bit like a track/bloodhound on any strange thing. Turbulence, Warnado and Shockdrive I’m not super sure on yet, though they’re the three that have the least build on them at the moment.