[exim] looking for spam in Exim log file - appended

Hi,

I'm wondering what would be typical (if I can put it that way?) log file
entries if someone was able to send spam through my Exim (4.43) server,
without me knowing it, and what would be the (best) way to block/stop them?

As far as I know I've got my server configured to send and receive mail only
for my (local) domains, but I've got a static IP, and when I try to send
mail to some people at AOL.com and mybe even Hotmail.com, it gets rejected
with a message about blocking spam (error codes 554 for example). I don't
understand why?

Thanks for all info/help!
Robert