All I can suggest is go through your settings and maybe make some changes on both the router and the PSP- maybe set up an IP address specifically for the PSP in the router's DHCP settings and put as much information into the PSP's settings manually (the Ip address, router IP, DNS servers, etc.).
As for the iTunes music, they do need to be converted to MP3 but you don't necessarily need a converter (which may not work on the purchased music anyway due to the DRM). All you really need to do is burn the songs you want onto a CD as a normal music CD then rip that CD as MP3 files in Media Player. Then, just transfer those MP3s onto the PSP.