Noob Question

I have not used git yet but am planning to. I am trying to get my head around how it will work and the documentation I found so far is of modest help. I currently have a Java application developed using Eclipse on Windows. However, the project is located on a Linux shared drive which is my Eclipse workspace. I do my builds using ANT on the Linux host. My main questions center around the git repository and accessing it.

1) Should I install git on Linux or Windows or does it matter?
2) How will my build scripts access the source? Will it be the same as
now (my scripts 'cd' to the Eclipse project directory and run there) or
do I need to add a wrapper to my script to check out the entire source
for the builds?
3) How do I move my current Eclipse project into git after I create the
empty repository? I can only find info on how to import git into Eclipse
not the other way around.
4) Do I need to checkout the entire project from Eclipse to modify and
test it or only the classes I want to change? Does the plugin get the
others as needed when I run the app within Eclipse for testing?

Thanks for any help understanding how I need to configure all this.