(1) How can I be sure my new domain has been approved and is active?

(2) For now, when I try to access by first page of my website, I only get the coding, not the images.

(3) when I bought my domain, it gave me the title:
epworth.name . Am I correct in assuming I can use epworth.com, .net, .org etc as I see fit?

Your domain is: epworth.name not epworth.com, epworth.net, epworth.org, etcv., etc.

All the others either owned by someone else or not at all.

Your domain is active and works. All you need to do is upload your webpages. Right now, all I can see is a word processor document that you appear to have uploaded by mistake, or possibly thinking Microsoft Word 11 should be used as an editor. There are hundreds of better programs out there, many of them free.

to sum up the above,

the different domain endings (com, net, etc) are all separate individual domains. if you bought the one ending in "name" then YOUR domain ends with "name". here is your site...
http://www.epworth.name/

as for creating/editing pages, a proper editor should be used. "word" is not very good at making webpages. it would be a lot better to use an online editor or download one such as NVU. learning some html and css coding would be really good too.