يا بتجي صاحبتك الاحد يا الاثنين، لانه انا مشغول السبت.

Here يا ... يا ... means either ... or ....

So:

• يا بتجي صاحبتك الأحد
• يا الاثنين

means Either your friend comes on Sunday, or on Monday.

This يا ... يا ... pattern is common in spoken Arabic. It is different from the more formal Standard Arabic pattern إمّا ... أو.

No. In this sentence, يا is not the vocative particle.

Arabic يا can do more than one job:

• يا أحمد = Hey Ahmad / O Ahmad → vocative
• يا هيك يا هيك = either this or that → choice/alternative

So in يا بتجي صاحبتك الأحد يا الاثنين, both instances of يا are part of the either ... or ... structure.

بتجي means she comes / she is coming / she will come, depending on context.

In Levantine, the prefix بـ on the imperfect verb is very common. It often marks:

• present
• habitual