Transactions and PHP and persitent connections

I've posted this to the PHP-db list also, but I find the people on this
list usually more precise in their answers so I was hoping someone here
might be able to help me.

I'm a little confused/worried about database transactions, persistent
connections and PHP. (Of course I am using postgresQL :)

I am worried that if I use persistent connections it might be possible
for more than one PHP script to be inside the same transaction at the
same time.

For example:

1- page1.php is a script that opens a persistent connection to a DB and
starts a transaction.

2- User 1 goes to page1.php

3- User 2 goes to page1.php

My questions:

1- is it possible that user 2 will be using the same connection as user
1? So if user 1's transaction fails so will user 2's?

2- If user 1's hits the stop button on his browser, what happens to his
transaction? I assume it is stopped. But what about the connection? If
user 2 gets the same connection, will his transaction fail?

3- If I don't use persistent connections, do all my worries go away?
I've abstracted the DB layer out of my code, but one side-effect is that
each SQL statement causes a new connection to be made. If a script
wanted to do the following:

BEGIN;
INSERT into t values('1');
COMMIT;

my code would actually create one connection per SQL statement. PHP is
supposed to re-use the same backend if a running script open a new
connection with the same parameters but I am worried that it doesn't,
and so transactions may fail.

I've never used transactions before, and even though they are a simple
concept, I'm worried that going through PHP might result in unexpected
behaviour.

Thanks,

Jc