Duplicating structure & themes on separate domains

Hello!! New to wordpress – haven’t actually started using it yet but considering jumping in with a new client, just a couple things I want to check that I can’t see in the FAQs…

First up, the client wants essentially the same site structure for two product lines on two separate domains – once I build one will I be able to grab the whole site and move it to a different domain, then simply alter the content??

And from the reading I’ve done it sounds like wordpress recommended hosting providers are preferred – will there be any problems or limitations to using a non-wordpress-recommended provider??

Thanks so much!!

Dannyrus.