Also I see the forum is loaded on top of your website. Please make the "Enable Output Buffer" option is enabled in Dashboard > Forums > Settings > Features Tab. Then delete all caches.

I need the forum to be full page and overwrite the theme for the /forum domain.

If the /forum is a separate WordPress installation you should use either Set Forum on Home or Turn WordPress to wpForo option.

Essentially I want what this site has a their forum:
http://www.doesntgrowontrees.co.uk/community/

And home page as:
http://www.doesntgrowontrees.co.uk/

As you can see the two are different.

When I turn the "Turn WordPress to wpForo" option on it changes my homepage to the forum, however I only want the 'domain.com.au/forum' to be the full page forum.

If I set up a subdomain like this:
https://smallcaps.com.au/forum/

And home page needs to stay as:
https://smallcaps.com.au/
With the same content on there.

It wants to put another forward slash item '/something/' in the domain.
So ends up being:
https://smallcaps.com.au/forum/something/name-of-topic-forum

Rather than how I want:
https://smallcaps.com.au/forum/name-of-topic-forum

Not sure how to do it but the 'doesntgrowontrees.co.uk/community/' has it and the link looks much neater.
Please help.