Should I look through all of your posts for the tools we've used??
No, you should see any left over programs on your desktop but Defix should have removed all the ones we were using.
Java.... not sure 'exactly' what it's used for? Games? Videos? Do I have it/should I keep it/what would replace it?
It is a program to help your computer see some web sites. Not quite so important nowadays with the modern browser abilities but still needed on some sites.
You do have it on your machine. It shows in your logs.
You can disable it in Firefox by going to Firefox > Add-ons and click on Plugins and press the Always Activate button and in the drop down click Ask to Activate (if Firefox has not already done that for you). You can then activate it when needed. That's how I have my one set up. I very rarely need to activate it.