Why rikai chan has so many readings in base? For example i open random book and i see:

 館 [やかた, たち, たて]
(n,hon) mansion; small castle; nobleman; noblewoman; boat cabin

 館 [かん]
(n,suf) house; hall; building

 館 [むろつみ]
(n,arch) inn

which one is correct? I suppose all of them are but... -.-

It depends on the context. The last one is archaic so you're not going to see it often (that's what "arch" means). The middle one is a suffix so you're only going to see it in compound words -- 図書館、　旅館、etc.

やかた　is the one that means "mansion" and the most common reading for the word when it's by itself and not in a compound. たち　and たて　may be archaic too -- at any rate, they show up in my archaic dictionary but not my regular dictionary.

Rikaichan is not really smart enough to know for sure what it's supposed to be in any given context.