For your first question:
You could install a modification that will allow you to customize the NavBar tabs near the top of the site. There you could add a tab called "Home" which will redirect your users to the WordPress area of your site without the need to re-type a URL. For example, the following mod would allow you to do this:
https://vborg.vbsupport.ru/showthrea...highlight=tabs
Alternatively, you could do it without mods and do it through Template Edits but I suspect you'd rather go for the less hassle method which is described above.
Second question:
The site logo is located in your
/forum/images/misc directory and is called
vbulletin4_logo.png. That is the logo that appears on the forum for other users. Simply create a new logo, rename it to
vbulletin4_logo.png and replace the existing one in the directory and the new logo should appear.
Feel free to comment back and I'll gladly assist you further.