The flat roof doesn’t suffer water ingress during heavy/violent rain, only because it is a single sheet from end-to-end. This means if water flows backwards, it doesn’t go under another sheet, or under any flashings.
The asbestos, fortunately, is in good condition. The advantages: will not burn, does not rot or absorb moisture. It makes modifications a little more time consuming (adding power points, etc), because I have to do a lot of preparation and wear the right PPE, but otherwise it’s not a hassle to live with.
To give you an idea of cost, we paid AUD$1100 to have four panels (two inside, two outside) removed + disposed, and replaced with modern cement sheet. (Reason for removal, was so that a split-system aircon unit could be installed on that wall. Removing the asbestos first, meant that the electrician and aircon trades wouldn’t have to cut asbestos.)
Good luck, stranger! :)