Calculix also runs on Windows but you do have a lot more options with Linux than Windows. You might want to look at CAELinux too, you can put that on a USB and boot into it without the need of installing Linux.
I recommend signing up for a class if you really want to learn this stuff, unfortunately though, not sure there are many faculty that know how to run modern tools like software...
When I first started to learn FEA, My instructor swore by doing hand validated calcs. I can see why. Software is very easy to use. . . and even easier to miss-use. If you really want to understand FEA, you need to understand Matrix math. Then you will have a good appreciation for what the software is doing and how boundary conditions can drastically affect your outcome.
I think hand calculations are often seen as too angelic, you can just as easily get a completely wrong answer. You forget a step, you invert the wrong sign, you get some trig wrong...
I think FEA isn't much more "automatic" than manual hand calcs, because setting up your loads, setting up your restraints, defining the mesh... all of that is manual.
The only automatic process is the actual number crunching (which is what a computer does) and as we know but a layman may not, it is not a black box. You do have control.
It's pretty much as manual as a manual hand calc. just then, in a completely different way. It can be valuable in that respect though, if fea and a hand calc. come out with similar answers because they are different in how one postulates the question and comes to a resultant answer.
