1 cleverly
I think 'voluntarily' is even better.
It means out of free will ,in contrast to them relying on their teacher's directions in the special class. I thought of 'cleverly' also because it is dependent on their free will and and therefore an independent way of thinking ,so that is clever ,specially that the problems are not on the school program.
However 'voluntarily' seems more appropriate for this context,because the sentence demonstrates their attitude in the special class opposed to that in the regular class, and it is likely to use opposites in such a context ( relying on teacher's direction versus reflecting voluntarily on the problem.)
3 interested
Look at the previous sentence:
" Many are concerned that gifted children become bored and lose interest in learning."
Then it is mentioned next ,that those are the parents and teachers and that most of those are adults .
Since those adults are not very much convinced of the idea of special classes for 'gifted' or 'talented' children, so when it is said that they conclude that those classes should be set up for a category ,it can't be the whole category of talented children .They think that it shouldn't be for all talented children, but only for those who are interested or whose parents are interested.