This is strange; the subscription you get as a student (which is now the same as a personal yearly plan) should include everything. If you can't find a download for ArcMap, I'd contact ESRI's customer service. It's useful to have both installed, but it's not required, especially if you don't have a preference for how some ideas work in ArcMap vs pro. In any case, the larger potential issue is not having access to licenses for extensions such as spatial analyst if you did not receive everything.
In terms of training, ESRI has some excellent tutorials. The simplest way to find them is to Google them - their "getting started with arc pro" page is very helpful and straightforward. I believe they have other recommended tutorials listed with the getting started stuff after that.
