No games will update your Xbox 360. When you insert a game and it asks you to update, this is a game update.
specify
yes
yes
No you can not.
yes you can you need to for it to work
The Xbox 360 can only play certain Xbox titles. A precise list of which Xbox games are compatible with the Xbox 360 is available on the Xbox website.
all can but most you need to manually update your Xbox the halo games and be played on Xbox 360
conect the charger to the xbox
yes it will but you may have to update the 360
Microsoft maintains a list of titles that are forward compatible with the Xbox 360. If the title you are trying to play does need an update to play that update will be applied when you first launch the game assuming that your Xbox 360 is connected to the internet.
download the updates from the official xbox 360 website then burn them on to a data disc then put the disc into your xbox 360 and install the updates.