113 is set to closed because it's the identd port. identd was an ancient service for 'identifying' yourself. The reason to set it closed not stealth is that many IRC servers still look for a response on the identd port before letting you in. No-one runs identd any more, but IRC servers still look for it, for some bizarre reason. If you set the port to stealth, than when you try and log in to IRC it'll sit there for several minutes before the identd check times out and lets you in.
As antman says, I think if you raise the security level, it will change it to stealth.
and yes, it's probably a good idea to open a port for transmission. See what port it's set to use (you can see in its preferences) and open that port. If you use a router, you will also have to forward that port through the router to your system.