Welcome to PSP3D. Here are some answers for you

(1) You cannot run emulators and homebrew on the official Sony PSP firmwares. you need to go to a custom firmware

(2) If the video is the right format you just put it in the video folder on the memory stick and it'll play. some movies you might need to convert to play so I would download a converter like PSPvideo9.

(3) Firmware updates add new cool features to the PSP sometimes but other times they are just stupid security update to stop homebrew and stuff so I would not update unless there is some great new feature coming to the PSP in the update. If you decide to use a custom firmware it's a bit different

and to your last question. No that stuff should not affect playing online

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