You don't need to connect anything for wireless, thus the name: wire
less You just need to go into the configuration and have it detect your wireless network (for which you will need the security info, WEP key or whatever your router uses). You can also do wired just by plugging it in.
I've left mine on for a whole weekend so it could do some folding without issue. Should be fine, though I wouldn't watch a movie right after having it on for that long.
When there is an update, it tells you that it is available and actually won't let you log into the network (you can still use the PS3) until you update.