Learn Dutch: Schenk jij even de thee in? - Will you just pour the tea?

The modal particle even softens the request. Without it, Schenk jij de thee in? sounds a bit direct. Adding even makes it sound like a quick, friendly favor, translating roughly to "Will you just pour the tea?"

Why is the verb split into Schenk at the beginning and in at the end?

This comes from the separable verb inschenken (to pour). In a main clause like this question, the verb splits. The conjugated part (schenk) goes to the front, and the prefix (in) goes to the very end of the sentence.

Could I use je instead of jij here?

Yes, you can. Using jij emphasizes the person ("Will you pour the tea, instead of me?"). If you just want to make a general request without that emphasis, Schenk je even de thee in? is completely natural and very common.

Why is this phrased as a question instead of a command like Schenk even de thee in?

Phrasing a command as a yes/no question is a common way to make it more polite in Dutch, just like in English. Combined with the particle even, it becomes a very friendly, casual request rather than a direct order.