Will I ever be able to play some classical music?

[trickybily]

1)  I had 2-3 years of very laid-back piano lessons in elementary school. i haven't learned ANY music theory I just played some religious music pieces only (the teacher was very bigoted). I learned to read some sheet music.
2)  Now, I am returning to the piano as a 35 years old. I learned for some months using Synthesia (only reading sheet-music and NOT the falling notes) since it could correct me if I played the wrong notes. I can play easily, flawlessly pieces like this:

and play SLOWLY, with around 5 mistakes (although with practice I am sure I will play it without mistakes and faster) pieces like this:

I have completed some basic music theory course on Youtube and memorized 90% of it.
Now I found a piano teacher and we will start lessons in two weeks.
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?

[j_tour]

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."

[quantum]

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?

Of course you can.  Focus on leaning new things about music rather than counting mistakes in your playing and using that to judge progress. 

[lelle]

Sounds completely reasonable to me. There is a lot of very playable classical music that does not require years of training to be able to handle!

[ranjit]

You can, for sure. I think many serious amateurs who start before they are 50 or so can reach a grade 6-7 level at the piano eventually.

[bwl_13]

Just like everyone said I'm sure you'll be able to reach a level of playing classical music that's really enjoyable. It might take a few years and you need to be willing to practice but I don't see why you wouldn't be able to play music that's enjoyable. You have a teacher now and with practice you'll be playing some sonatinas and bagatelles in no time. I've heard of pianists that started in their 50s and were playing Chopin etudes 10 years later. Good luck, or more accurately, study hard!

[brogers70]

You can, for sure. I think many serious amateurs who start before they are 50 or so can reach a grade 6-7 level at the piano eventually.

Definitely. Grade 6-7 is certainly doable (I've done it and I started at  age 40, 20+ years ago) and there's lots of good music at that level. With a good teacher and lots of good practicing, I think you can get farther than that, say up to the less difficult of the Beethoven Sonata's say - I've managed to play the Ab Sonata that starts with theme and variations, Opus 14 number 1, and the first movement of the Pastorale in small performances without embarrassing myself. So definitely, have at it. Make sure you are enjoying the process and are not aiming at something so far beyond your current level that you get frustrated. Enjoy playing easy things well, and the more difficult things will come in time.