I don't know your users, so I don't know what they will think of having the breadcrumbs barely visible.

To move the logo to the right, increase this value:
To move the tabs to the left, change the padding (specifically, the left padding, so 0 20px 0 0):

Without sounding too amateurish, what does this mean? I am afraid I don't understand what breadcrumbs are in respect of VB forums.

And thanks for your help in respect of the header - I should be be able to get it how I want now.

Breadcrumbs:
http://puu.sh/bfokt/c54219efda.png

The breadcrumbs are the little house image with "Forum" after it. If you go to another page, it will have the path like the image Dave posted (although his is a vB3 image).

Thanks.

And I have done a search for this but cannot find any guide/post that is applicable or matches the code, so I would be grateful if you could advise how I:

1. Remove some of the sub-links (FAQ, Community, Forum Actions, and so on)?

2. Move the white search bar somewhere less obtrusive or remove it altogether if that is too difficult.

On a default style, links are modified in Admincp > Settings > Navigation Manager > edit link . You have a custom style and it could be that those links are just hard-coded. You can try getting rid of them in the Navigation Manager, but it that doesn't work, you'll have to find the template where they are and modify it that way.

The search bar is something you would need to modify via a template also (or you may be able to set display: none for both .globalsearch and .advanced_search).