immaculate if your contract is for 16 hours why are you doing more, can you not refuse overtime?
You do have a right to request a change in shifts, your employer doesn't have to agree if they can demonstrate good business reasons why they can't accommodate your request.
It's certainly not reasonable to expect your employer to agree or not agree at such short notice, there is a procedure you have to go through and they have the right to consider it properly, discuss it with you, discuss alternatives if your initial request isn't possible, etc
There aren't actually specified time limits for disciplinaries but it wouldn't be considered reasonable to suddenly decide something that happened 2 months ago needed a disciplinary. If they'd said to him at the time that they were going to do an investigation with a view to a possible disciplinary, that's fine, but if they suddenly decide to discipline him now that wouldn't be reasonable and he should appeal it. If they think he's not getting enough rest they should address that rather than discipline him!
With regard to your request, here is some information about flexible working, whether you're entitled to request it and how to go about it.
I'm not convinced about the tax credits argument tbh, your benefits situation isn't really their concern although if you have a nice sympathetic manager it might be worth having a word about that. I think marching in with evidence of that isn't going to help though. I think the issue is why are you not already sticking to your contracted hours? You need to have a think about that and sort that out as well as requesting the change in shifts you want.