I use Fasthosts to do all the things you asked about, Rev. At the time that I registered my site they were a local company and it seemed a good idea to support them. They're very good - but there are a thousand company that provide the same services. So I registered domain names through them, rent web space through them, and could use their web-builder functionality if I wanted. For the latter, I simply do it all myself and upload the files through FTP, which is dead easy.
So to answer the questions: yes, you can set up your domain to redirect users to any site, and you can set this up so that it masks the original domain. So if you had current pages at free.web.pages.rev_a.org and you bought rev_austin.co.uk, you could simply redirect the former to the latter and no-one would be any the wiser.
You buy/rent web space, load your pages on to it, and then link those pages to your domain name, just as you've outlined. I've never used the site building options offered by Fasthosts but I'm sure it's easy. But your web space supplier will provide the details of how you upload your pages and it's very easy to create your own or download free templates from the web. As said above, I rent space from the same people I used to register the domain name, but this isn't a must.
Registration is indeed the buying/renting of a domain name. You normally renew every two years so it's never really 'yours'. You can do this through a thousand companies - it's big business; and once you have a name you find someon to rent you webspace, and away you go. You can pay for extra options on the webspce if you want - database functionality, options to build active code pages, etc etc, but I just go for basic webspace. Simple really.... It does make it easier to use the same company for all this stuff, but it's not a must.
Kind regards,
Del