Using pgpool and PostgreSQL in differents hosts. I want to use pgpool but I did some research and I have a doubt, if neccesary install PostgreSQL and pgpool in the same machine? When I did my first configuration and installation in a same host. But this gave me some problems, some time Postgresql services can't start and I want to separate them? It is possible?
They do not have to be on the same host; otherwise lots of the useful things you can do with PgPool-II would not be possible.

PgPool-II communicates with PostgreSQL over PostgreSQL's TCP/IP protocol.

The reason it wouldn't start on the same host is probably because you were trying to run both PgPool-II and PostgreSQL on the same port (5432).