***** NOT A TEACHER *****
(1) I believe that No. 1 consists of two sentences:
I wonder something. + He was hinting at what when he put my shoe
next to the garbage bin?
Therefore, together we might have:
I wonder what he was hinting at when he put my shoe next to the
(2) I believe that No. 2 is not idiomatic. That is, I believe that most
native speakers would not speak like that. Maybe it would better to
say something like:
What was he hinting at when he threw my shoe away?
If you wish to use the expression "drop a hint," then maybe something
like this is possible:
Was he dropping some kind of hint when he threw my shoe away?