Learn Dutch: Zal ik langskomen en jou oppikken voor de borrel? - Shall I drop by and pick you up for the drinks?

Zal ik translates to "Shall I" or "Will I", and it's the standard way to offer to do something for someone in Dutch. Because ik is singular, we use zal instead of the plural zullen. It acts as a modal helper verb, which means it pushes the main action verbs to the end of the sentence as infinitives.

Both "langskomen" and "oppikken" are separable verbs. Why aren't they split up here?

Because of the helper verb zal. When you use a modal or auxiliary verb like zullen (or zal), the main verbs are pushed to the end of the clause and remain glued together in their full, un-split dictionary form.

Do I need to repeat "zal ik" after the word "en"?

No, you don't! Just like in English ("Shall I drop by and [shall I] pick you up?"), the zal ik at the beginning applies to both parts of the sentence. The word en (and) simply links the two infinitives langskomen and oppikken to the same helper verb.

Why use the stressed pronoun "jou" instead of the normal "je"?

Using jou instead of je adds a bit of emphasis. The speaker is highlighting that they are offering to pick you up, making the offer feel a bit more personal or direct. Using je would also be completely correct, just slightly less emphasized.