Is there any way to have two applications visible at the same time, with one application not in use overlapping the other
What you're looking for is the option to "float" apps. 
Before I give my answer, I should say that you need to do a bit of Google on "How to keep apps on top on mac" 
With this, I found that this was already mentioned before in superuser.com
If you are too lazy or have slow internet, the answer mentioned was Afloat, since Afloat is open  source, install guide here.