dpkg: error: parsing file '/var/lib/dpkg/available' near line 0

The problem is that your /var/lib/dpkg/available file is damaged.

This is not necessarily related to the git or git-core packages. Try to install any other package and they will fail too.

To fix this you have to delete/clear the file using the command:

sudo dpkg --clear-avail

then rebuild the file using the command:

sudo apt-get update

Now you should be able to install git and git-core.