3) I only love and listen to classical music. My question is that will I ever be able to play at least the easier kind of classical music on an amateur level for my own pleasure?
I don't see why not.
Just look for yourself at things like some of the Beethoven Bagatelles or some of the Schumann Kinderszenen: it's not too far off from your example in 6/8 time, some of them.
And there are plenty of easier works as well.
Just go for it. I wouldn't say this type of LH=chords and RH=melody is beyond your grasp, and there is a great deal of legitimate music written in this kind of fashion.
There's much more, but you have to start someplace.
I assume "Synthesia" is some kind of app/game. Time to put that kind of child business aside and start reading and playing music, I should think. Sheet music, and if you need feedback, your teacher and recording yourself is plenty. No need for little kid "apps": you're well on your way to being a real musician, so you can use adult tools. Viz, pencil and paper, and your own ears, along with the ears of others.
And I don't understand the "counting mistakes" aspect: are you playing music or taking an exam?
Play music. Make it sound good. Like somebody said once, "Nobody ever got fired for playing a pretty melody."