No it does not have to but it it is recommended!
yes you can surf the internet on the xbox 360,just google it down or something to learn how to do it
No, you have to use your gamertag.
To connect the different players on Minecraft xBox 360, you will need to use the split screen.
i know how to do it on the 360 and i use horizon.
Yes, there is split screen on Minecraft Xbox 360 Edition, but it is exclusively for the use of HDTVs, so far.
you can but it has hardware to it
Yes
Use an infinity bow.
Yes you can!
No, mods are only available for the PC version of Minecraft. You can't run or use unauthorised data on an XBox 360, only things officially authorised by Microsoft.
yes you can surf the internet on the Xbox 360,just Google it down or something to learn how to do it