Do I need a comma in "Тут есть, над чем подумать"? And can anyone parse this sentence for me, please?
The comma is not needed. Над чем подумать is the subject of the sentence, it's a verbal phrase, an infinitive with an indirect object. The verb есть agrees with it, it's singular, "Тут" is a predicative (I have some doubts about "Тут", it can be an adverbial modifier of place).