Are there free software tools where I can do mock testing?
There's lots. For starters, what software do you have on the machine that you're using right now? Any reason to not try testing any of it? You could always go grab a copy of some open source software. Nightly releases are great for practice. Is there any approach in particular that you're interested in?
Seeing that you say that you're looking for web testing, my own personal recommendation would be to install some sort of web debugger. Since you're using mac, Fiddler is out of the question, however, it appears as though CharlesProxy is an option. It should help give you a good understanding of what's going on under the hood while you're browsing/interacting.
I'm not entirely certain about apple products, but, if you have a windows machine, you can use the web platform installer to install applications locally to test on as well.
Keep an eye out for Weekend Testing sessions - a good way to learn testing and interact and learn from other testers