Learn Dutch: Wat voor zakmes heb jij bij je? - What kind of pocket knife do you have with you?

When a preposition describes a physical, spatial relationship to the subject (like having something on your person, or looking behind you), Dutch uses the normal object pronoun (me, je, zich) rather than the -zelf reflexive form. So it is bij je, not bij jezelf.

The subject is the emphatic jij. Does the object pronoun in bij je also need to be emphatic, like bij jou?

No, in these locative phrases, the unstressed pronoun (je, me, zich) is strongly preferred, even if the subject is emphatic. You would only use bij jou if you were making a specific contrast, such as emphasizing that the knife is on YOU rather than on someone else.

Does the phrase wat voor change depending on the gender or plurality of the noun?

No, wat voor (meaning what kind of or what sort of) is a fixed chunk. It stays exactly the same whether it precedes a het word like zakmes, a de word, or a plural noun.

Why is the verb heb placed right after zakmes?

In Dutch question word order, the finite verb must be in the second position. Here, the entire phrase Wat voor zakmes functions as a single question block occupying the first position, so the verb heb must immediately follow it.