Funnily enough there actually is an atari jaguar emulator for psp. I think it's just for proof of concept as it runs hideously slow (https://youtu.be/Q_2ALZteHfM
). In terms of the lynx there is an emulator called 'Handy PSP'. It seems to work okay but the audio is quite crackly and the games don't quite run at full speed a lot of the time (~95% speed). Also, roadblasters doesn't work properly :-/
In terms of the wifi there is no reason why it wouldn't find it at all?! I know a lot of routers that use some of the newer security protocols (wpa2 I think) aren't supported by the psp and display the message 'not supported' in the signal strength column.