ARS

Their bonus still applies, regardless if it's the same ship or not. Their bonus isn't just limited to a single ship

Are you using nuke engines? Nuclear engine generates heat, hence why the radiators are mandatory to avoid overheat if you want to do interplanetary burn with them
Or maybe, your engines are attached too close between each other? If your engines are clustered too close, the heat of the engine can affect nearby part, which could lead to overheat
Or you might be getting attacked by kraken. This is very common bug in KSP, which usually occurs on craft with large size, complex and huge part count, and especially, anything large enough created by connecting docking ports. Timewarping might cause flimsy joints or connection being misplaced and when the time resumes normally, it suddenly snaps to it's original position, often with catastrophic result (for an experiment about how time warp can cause explosion, make a plane or rover and drive/fly it then activate the timewarp. Sooner or later, it'll explode, the game even warns you about timewarping with large vessels since it might cause structural instability)

It's because your career mode setting. Normally, a tech node is unlocked with science point, which will give you an access to unlock parts inside that node with money. The money to UNLOCK parts is not the same with money to BUY that part. You cannot use money to unlock a part if the node is still locked. When starting a new career, there's a custom difficulty option that removes the requirement to unlock parts with money, so you only need to pay the science for a node, and all the parts inside that node is yours

You wouldn't want to use wheels on gilly. Last time I'm landing on that ball of rock with my SSTO, it wasn't treated like a landing, more like a rendezvous with surface
If you want to build a tanker for hauling stuff on gilly just slap a probe core, some reaction wheel, battery, antenna, RTG (or solar panel) and an array of RCS thrusters to move around. Trust me, when you use a wheel on gilly, most of your time will be spent making it move normally instead of hauling stuff. It's okay if you want to set up a mining base there, but generally, due to gilly's very low gravity, it's much more efficient to just use a lander as a miner and a tanker. It doesn't take a lot of Dv to get into gilly orbit
Anchoring the whole mining rig on gilly is a viable solution to make it stand firm as you do your mining operation.