1.) Is there an advantage to installing a forum on a completely separate subdomain? So something like http://forums.MyDomain.com/
I have noticed other people doing this.
2.) Are there any issues with integrating forums like Simple Press or BBPress with my WordPress Blog if it is on a separate subdomain?
One advantage is that you can have a separate user to manage the subdomain.
$50 off and 3 free domains with code: [color=#CC0000]DH3[/color] Sign Up NOW or More Codes Here
Are there any search engine advantages?
Search engines will find subdomains just about as well as domains. If the forum is integrated into your site, I’d use a subdirectory like /forum rather than a subdomain. If it’s a separate operation, then I’d use a subdomain.
What are the advantages and disadvantages of making it a subdirectory (/forum) as opposed to a subdomain (forums.site.com)?
Using /forum keeps all relevant domain files in one primary domain directory.
Makes it a bit easier for backup procedures.
If implementing a subdomain you would be presented with 2 directories in SFTP:
Maximum Cash Discount on any plan with MAXCASH
How To Install PHP.INI / ionCube on DreamHost