A party may object that the arbitral tribunal lacks jurisdiction, and do so in time. But they may give up this objection by their conduct. If they take active part in the proceedings - for instance, by making settlement proposals to resolve the dispute amicably - they cannot later maintain their objection.
When the Supreme Court reviews a judgment about a challenge to an arbitral award, it cannot look directly at the arbitral decision itself. It may only examine the judgment given in the challenge proceedings, checking whether it follows the law and is properly reasoned in relation to the grounds for challenging the award.
Where an arbitral tribunal finds that one party has partially admitted the other's claims during the proceedings, it may properly make an award condemning that party within the limits of what was admitted. It need not simply declare that there is no longer anything to decide, unless the parties have reached a complete settlement agreement.