What are the components I need for assembling a hobby mobile phone?
Way too broad. Do you mean individual parts, like specific ICs, etc? Or do you mean high level, block diagrams? A hobby device is exactly like a commercial device.
How would I go about assembling such a hobby device?
Again too broad. There is no one way except "Soldering"
Are there laws governing assembly/use of such hobby devices?
We are not lawyers. And most likely, noone here has built a device like you intend, so they haven't done any research on their own. And laws vary by county, state, federal even international levels. Only a lawyer or paralegal would have a clue of where to even begin looking up documents.
Can I flash the ROM of a mobile phone, e.g. Nokia, in order to install a custom minimal operating system on it?
Yes. And a specific question on how to do that like "I have xyz rom. I've check the datasheet but can't be sure. Can it be flashed?" is good. A general question like "I have a nokia 3620. I can hack it?" is not.
Which peripheral/main units can be used to check a firmware's digital signature?
A computing question, at best. Not EE. Off topic.
Can someone point me to an appropriate SE site or a related SE forum? I'm hoping for a site with about as much users as this site has.
There is no other SE site that is close to EE for electronics question, and most of the other questions are off topic on most of them. Sorry.