Do you think I have above average abilities learning piano by myself?

Okay, this is not to boost or to make myself sound good. I was just
reading some articles and came to this site explaining that you really
need a teacher, lessons, books, training to play a sonata or any
classical piece.

I started playing a classical well at the age of 11, and was able to
play at the age of 7. My grandmother just told me the positions of
notes, not the beats(which i discovered by myself) I began playing
pieces the fair/proper way(with right beating) at the age of 18.
(SINCE I just self-studied)

Now, I can play tocattafugue and Bachs Inventions(with proper
fingering). All I did was I studied Hanon, other books my grandmother
left, read, read and read on the internet. tried to listen how each
note is to be played. And thats how I reached to the point that all my
fingers are working and can play on the right beat of a piece which is
not that advanced like Invention.

I'm asking these because I want to understand myself. I sometimes feel
I'm not good at something, but everytime I remember how I learned it,
I feel like I've abilities. I also write simple programs.

I just love teaching myself by reading and observing.

You think I've remarkable abilities/ above average IQ/ability learning
the piano by myself? Or am I just over believing???

Any answers would be appreciated. Thanks =|
Also learned guitar and some violin by myself??? Maybe because of my
interest.?? =/