You can challenge the impartiality of Arbitrator but that will not automaticaly debar him from conducting the proceedings. He can pass an order rejecting your challege and proceed and there is no appeal against such rejection.
As per Arbitration Act, the Arbitrator can ask both the parties to deposit in equal share the likely cost of arbitration including his fee. If you refuse to pay, the other party may pay your share and continue with the proceeding but then it will be recoverable from you against the award or in addition to award.
You can only challenge the final award citing the reasons of bias, opportunities not being granted to you etc. But at this juncture it is advisable that you cooperate with the proceedings while briniging your objections on record. Please note that the award on arbitrator is executable in the same manner as of decree of court unless set aside by a competent court.