How does a domain beginning with www.uk get resolved?

I have seen domains such as www.uk.domain.mobi. Is there no restriction in terms of what is allowed after www?

Can I call a subdomain anything I like and is there no dot-separated word limit?

No. At the very least after the second level domain (domain.mobi) you are completely free to choose additional subdomain names. Even www is such an arbitrary name. Of course, your local laws might restrict you, and there are some technical restrictions:

• max.127 levels
• max 253 characters for the complete name
• 63 characters for a sub-name (like www).

See this for more infos.

Simply put (in addition to restrictions mentioned in other answer):

www.uk.domain.mobi
|      |     |
|      |     .mobi - TLD (Top-level domain) => Currently ~253 to pick from
|      |
|      domain.mobi - Domain name => Can be anything that hasn't been registered
|
www.uk. - Sub-domain(s) => Can be anything you want after registering the above.

List of TLDs

Can I call a subdomain anything I like and is there no dot-separated word limit?

Yes, once in control of the DNS records you can create subdomains, sub-subdomains, sub-sub-subdomains, etc.