He would remember his expression, remember the tears starting to well up in dark green eyes, and wonder.
Is the "wonder" here a noun or a verb? What does it exactly mean?
From the context, it's a verb. Though it could be a noun, particularly if that last comma wasn't there, it could mean "he would remember his expression, remember the tears, and [remember the] wonder".
But I'm pretty sure it's a verb.
In this case it means "and he would wonder", which means he would be deep in thought.