I’ve never ever charged an hourly rate and don’t know any other composer who does (except tiam! haha), though I’m sure they exist.
Most mixers / mastering engineers I work with work on a per track / per album basis.
Recording studios usually charge by the hour, but you’re much better off booking a whole day as it’s usually cheaper and a bit less stressful.
Most composers I know vary their fees depending on the project. Many of them charge a creative fee per minute of music, and then a production fee on top of that to cover live musicians. I charge $1,000 per minute of fully-produced music, more if the project needs live musicians. Some might say that’s a lot, but it really isn’t.
In my opinion, it’s much easier to set a fixed fee, because then you know what your budget is going to be for the whole project and you can plan accordingly. I personally don’t believe that music-creation is something that can be ‘metered’. I’ve had movie trailers go up to 12 revisions and I’d feel like a punk if I kept charging them hourly, but that’s just me.
As for arranging, I’d charge by the song or if it’s an album, I’d look for a set fee for the whole album. If also depends on what exactly you’re arranging the instrument for. Are you arranging it for a band? For an orchestra? There are big differences.
In short, you should expect to be paid what you think you’re worth, but there is no rock solid answer to that.
You might find this useful, I wrote it a while back along with some contributions from other AJ users.
Note that there is no ‘correct’ way of doing things, but you will find very quickly what works for you and what doesn’t. There is also no correct price for anything. You will find people that work very cheaply, and you will find people that want $20,000 to master an album. There are just too many variables. If you’re good though, people will usually pay.