I am wondering if it is possible for other users to see your IP Address, or to see the IP of the person that submitted the post.
Other than moderators (and people working for SE) - no one can. Moderators have to agree to a moderator agreement, and have their viewing of IP addresses logged.
So no, it is typically not possible to do either unless you have a good reason to.
Also, IP addresses on their own are pretty boring.