What about SSI - or Server Side Includes - function by which we can let our forum and our website interact with each other.

I think you are talking about this:
http://en.wikipedia.org/wiki/Server_Side_Includes

That is a very unsafe way of interacting and all this is provided by PHP by default.
What interaction are you looking for by the way?

To make blocks of latest posts, recent posts, top poster, To show last posts of some specifics topics, latest topics, top topics, new members

Actually portal can do all these work, if u will make one portal

To make blocks of latest posts, recent posts, top poster, To show last posts of some specifics topics, latest topics, top topics, new members

Actually portal can do all these work, if u will make one portal

The way how Codoforum works solve the problem of a portal or a blog. The emphasis here is on the content- posts and topics (not like the regular forums where you have onscreen a bunch of notrelevant informations) You don't need them anyway. The Forums are about the community and everything else will be ignored from the users. I know this because I own forums since 10 years now. The best way is to have averything inside the forum. The suggested "BoardTypes" solve the needs in cases when someone needs something more than just a typical forum.