My ex wife has supervised vistation, and she hasn't been over to see our daughter in over 2 months, nor has she sent money, or paid for anything for over a year. What should I do? Is that child abandoment?

Actually abandonment in Georgia has nothing to do with visits or seeing the child. It has to do with paying court ordered child support.

So if she has court ordered support and has not paid in over a year, you report this to child support enforcement, contact the DA about child support abandoment and you may also take her back to court to try and collect.

Sometimes sitting for a couple months in jail may get them to start paying when they get out, but also if she has income child support enforcement should be able to get it also

She doesn't keep a job long enough for them to do that, my second question do I have to set around on the every other Sunday morning waiting for her to show up? When she hasn't in the last 6 visits?

You need to go back to court and see about getting her visits changed. ( reduced)
Also who is doing the supervision ? Normally should be a third party