This thread has long needed some answers and I will try to provide what I can after winning as a researcher on Belitlli.

Solar Core Taps are ships (not orbitals, despite the stats showing in game), and thus, they are mobile. They are slow, but not overly so. I did not clock them, but they seemed to move around the pace of my battleships (though again, I'm not entirely sure). In any event, I never felt like they took too long to move from system to system and they do not have to be built in the system that they are to be used.

Solar Core Taps must be placed in the orbit of the star (not an orbiting planet) before you have the option to turn on the core tap to create a black hole. If you have researched hyperspace physics your ships will be safe in the system with the new blackhole, but honestly everything happened so fast before the server came down that I did not really get to see how this all works. I wish I could tell you more here.

I believe the core taps can only turn a single sun into a blackhole until you research more levels of gravitron physics, in which case a single core tap can be used more than once.

I have no idea what the ascension device is, but I do not think it's part of the current game.