Is it possible to pull resources from sub-sites/contexts into one parent website?
Yes. Absolutely, as long as they are in the same installation. You can also get from just one context and discriminate if you like.
Can each sub website (they will be managed by different people) have (or appear to have) its own manager area with its own images folder (for example)?
Yes. You would have to set up an ACL (hard to learn at first), User Groups, Resource Groups and Media Sources for each. Then each will have its own area. Only full admins could see all of the contexts (sites) at once.
Is there a really good tutorial out there to get me started or is it time I bought Bob's book from Amazon (assuming it is available in the UK)?
There are many such good tutorials for lots of things, but they are hard to find sometimes. Bob's book is probably the best one stop shop. I have never read it, however, so I don't know if it addresses multiple domains. I'm sure it does, though, as BobRay is extremely thorough.
Any initial thoughts, guidance, warnings etc. would be very much appreciated before I just dive right in and screw it up.
You are in a new platform using a lot of new techniques for the first time. You'll screw it up. You should be happy about it and dive right in! Besides, it is pretty hard to screw it up in a way that it cannot be fixed really easily. MODX is extremely forgiving (believe me, I know).