Those are all DM extras. 5e inherently only has jump goes distance. What is on the other side could affect the DC, but it would be in addition to the DC for X extra feet which has no process. Is it enough for arms to grab on? DM extra that has no bearing on jump distance. Height? DM extra that has no bearing on jump distance in 5e as halflings with 10 strength go as far as goliaths with 10 strength.
Clearly success is making it across without falling from the athletics jump check.
These are also DM extras for the most part. How stable is the light fixture? Has no bearing on the DC of the acrobatics attempt. The PC either succeeds or doesn't, and THEN the fixture either falls or doesn't independent of the acrobatics result. How easy it is to grab onto is built into the DC of the pass fail attempt. The other circumstances involved with rigging on a ship are going to affect the DC number of the pass fail attempt.
I disagree. What can the PC grab onto? Can they grab on get a decent grip? How well do they judge, as they're swinging the momentum and movement?
The DM deciding DC numbers has no variability in the same manner as jump distance. Sure you are assigning a number that can be variable. Do you assign a 7 or a 9 for example, but once DC is determined walking along the ledge or rope is pass fail. Unlike jumping farther.
You answer all of them with simple numbers. Most are simple DC numbers. The exception is the stability of the fixture, which will probably involve a roll unless it's so unstable that it auto-falls without a roll of some sort, but it's not going to be a skill check as it's simple weight and force vs. stability of the fixture to determine if it pulls out of the ceiling.
In any case I use skill checks based on how difficult I envision a task all the time. I don't remember the last time I used it for jumping. The same system covers a lot of bases so it will never be perfect, nothing is.