is it possible to place the logo to the right of the "home" button?

The logo can be "big" and in the original location before the user logins.

But the big logo would disappear once the user logins.

A small logo is then visible on the left of the "home" icon.

Hi leevon.

Bassicaly everything is possible with some php modifications, however there are beyond our support scope, so there's not much we can do to help you. Maybe you should consider hiring a professional php developer for this task?