A few questions

First on prepared statements:

1) If I am using the libpq are prepared statements tied to a
connection?  In other words can I prepare the statement once and use
it on multiple connections?

2) What is the logical scope of prepared statement names?  Can I use
the same name on different tables without conflict or is the scope
database wide or something else?

On indices:

3) same as 2 for index names.  I think they are per table but it is
worth asking.

and last:

4) Is it generally better to have more tables in one database from a
memory and performance point of view or divide into more databases if
there is a logical division.  The reason I ask is that I have a
situation where one app is used by multiple different users each
running their own copy.  The app uses on the order of 30 tables.  In
some ways it would be convenient to have one big database and
specialize the table names per user.   But I am not sure that is most
optimal.  Is there a general answer to such a question?

Thanks very much for any enlightenment on these questions.

- samantha