Pensar si: to wonder whether; to wonder if

I wonder whether we could train parrots to interpret between birds and humans.
Pienso si podríamos entrenar al loro a interpretar del ave al humano.

“Wonder whether / if” is usually translated as “preguntarse” or “quiero / me gustaría saber.” I think preguntarse entails a self reflection or awareness that wondering does not usually and to want to know connotes more resolve than does wondering. Wondering is a very vague or loose way of questioning a topic—not to be cliché, but it is much like letting the mind wander. “Pensar si” is just as vague.
Unfortunately, things get a bit more complicated when you consider “wondering why…” Pienso por qué…? Honestly, I’m not sure.

Extrañarse que + subjunctive could work but it still seems a bit more specific than does wondering. It works when, as is often the case, the wondering is caused by an impression of strangeness, like wondering why some people keep ducks as pets, but doesn’t quite fit if you’re simply wondering why some true thing is true, like why there is something when it seems like there could be nothing. Or, like, why colors? Why are plants green? Why is chlorophyll green? Why does that frequency of reflected light cause a sensation of greenness, particularly?

*Parrot joke adapted from MBMBaM 504