Anybody with VPS Knowledge needed

First of all, sorry for the dumb questions, im completly new to setup a VPS.

Just a few Questions:

What is needed to run a VPS 24 Hours a Day for download/upload from Chrome or Mozilla Browser ?

Do the VPS Server need my local Inteet Conection for download/uploading ?

Is it possible to shutdown my Home Computer while the VPS is ruing online ?

I would pay for the Information - Already tried the VPS from google and "AppOnFly" (there you get a trial)
But it seems they need my local Coection to stay online (?)

I tried to upload Video Content and shutdown my Home Computer, the VPS Conection discoected - What i need to stay online with the VPS without home local conection ?

A Answer to this would help me alot,
Thank you!