Roche

AIB Garage Ceilings, Ive done a few garage conversions on my developments and they're super common on anything pre 90s

If its a house you're living in then id just get it removed not worth the risk to health to be living with it. Whilst cement roofing sheets are generally safe when left alone, these look to be deteriorating so I think its time for removal. You're most likely looking at around £25-30/m2 for cement sheets + scaffolding for an asbestos removal company to remove and dispose.

The insulation looks like Rockwool, but the fabric mesh looks suspect to me, Definitely get it tested before touching

Yeah doesn't really look like asbestos to me, but the only way to know for sure is getting it tested. Just search asbestos testing kit on Google or Amazon

Definitely get it tested before drilling into it, you don't want to be using power tools on it if its asbestos, even more so if its AIB. Id get a test kit and send a sample off to be safe.