Lighting – No place to put base for a ceiling lamp

Are hook-based lights common?

Not where I live, but Ikea sell them.

Can they be retro-fitted to fit onto a hook?

There's no easy way to adapt light fittings that are prevalent in my part of the world and which are designed to screw into the ceiling.

Of course, typical pendant lamps that hang from an electrical cord or chain would work well with the hook if you remove any ceiling fitting supplied with them. You'd retain that existing connector widget and its covering dome.

is there an easy way to install a fixture which would allow screw-based ceiling lights to be installed?

Not easily, especially in rented property.

If you speak to the property owner, you might be able to arrange a professionally installed solution.

That tube obviously supports sufficient weight for a modest lamp. I can imagine it should be possible to create an adapter - perhaps a wooden disk with a hole that fits over the pipe and is held in place by that bolt (which presumably attaches the hook). You might then be able to screw a normal light fitting to the wooden disk. I've never seen a ready made adapter (but then I've never looked for one).

I don't like to hear that you have a ticking sound, possible heat expansion. It is clearly not installed properly with old support eye still in place. I recommend a complete proper redo of hanging of the fixture. Make sure all connections are clean and tight. Get all obstructions out of the way. And no pinched wires.