Once you filed a cross complaint you agreed to the jurisdiction of the court. Dismissals based on lack of service are very hard to win if you were just to dismiss your cross compolaint and try to win on the complaint only.
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Most likely you filed an Answer with the Cross-Complaint, so even if you dismiss the Cross-Complaint you would still be subject to the court' jurisdiction. You cannot dismiss the initial case as a defendant but you can challenge the complaint for lack of service. At this point you may as well keep your Cross-Complaint on file and try to mediate a ettement with the small claims mediator. Good luck.
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No. Once you appear, service is irrelevant. You said you filed a counterclaim, I assume you answered as well. Two reasons service does not matter.
You can't dismiss it because you did not bring it. Call the plaintiff and offer to both fold your tents and retire from battle- you can get rid of the entire lawsuit that way.