Not really. In English you can learn an instrument, but in Polish you need to learn to play the instrument. Maybe it would be acceptable in colloquial speech to forget the playing part, but I wouldn't say that. Even then, it would be "uczę się gitary/skrzypiec" (Genitive). Better stay with "uczę się grać na skrzypcach".
And "practice" when you mean you're learning, is "ćwiczyć".
I'm afraid that's an overinterpretation. Whether someone is being taught or actually teaches oneself depends on the context.
For example: 'On uczy się w liceum' can't be translated by 'he is teaching himself at highschool'.
Of course, teaching oneself to meditate is possible, but being a Buddhist it's very likely that this person is being taught by a spiritual teacher. And I don't like the idea of deliberately excluding this interpretation.
If you wanted to emphasise the absence of a teacher, you could say uczy się sam or uczy się samodzielnie.
If teaching oneself is used in a contrastive statement or an enumeration you can also use the emphatic pronoun siebie:
He's teaching himself and others. - On uczy siebie i innych.