exim - changing smtp server ip in headers & send fail timeout

[Micha Feigin <michf@post.tau.ac.il>]

I am using exim as my transport agent.
currently its sending mail directly to the internet and is not using a
smarthost (I am not sure if this is the best option but works as long as
I am connected).
I have two problems currently.
1. Exim write in the headers the address of the server (not the from
field which is ok) which is my local networks address and not my gateway's
address. This way some hosts that check where the mail originated fail to find
the address in the dns and refuse to deliver the mail. How do I make
exim use something other then the real hostname?

2. If I am not connected to the internet exim fails to find a dns entry
for the target and bounces the mail instead of trying again later. How
do I solve this? should I use a smarthost (the problem is that I have
several possible from addresses and I am not sure that the smarthost
allows other then its domain in the address).
Is it possible to force exim to try to connect now (if I connect only
for a shot time ?) is this done on ip-up? (that way I can probably do a
/etc/init.d/networking restart).