There are two separate issues here and they should not be mixed: (1) challenge to the arbitral award passed in the SBI Card matter, and (2) territorial jurisdiction and maintainability of the criminal complaints filed by Kotak in Kolkata.
1. SBI Card arbitration
Your written objections sent to the email address specifically provided in the ODR/arbitration notice should not simply be ignored. If you have proof of transmission and the communication was sent through the prescribed channel, it becomes relevant material for the arbitral record. Whether it establishes an effective objection will depend upon the exact arbitration clause, the ODR procedure and what happened after your objection.
If SBI itself had the contractual power to appoint the sole arbitrator, Section 12(5) and the Seventh Schedule require careful examination. A contractual clause permitting unilateral appointment does not automatically remain enforceable merely because it was agreed earlier. However, the precise appointment mechanism and the nature of SBI's role in the appointment have to be seen before concluding that the tribunal was legally disqualified.
The fact that SBI subsequently changed its arbitration clause does not automatically invalidate an arbitration commenced under the earlier clause. Ordinarily, the clause applicable to the dispute and the date on which the arbitration agreement became operative have to be examined.
The alleged non-supply of documents and the fact that the award records service which you dispute can be important. If you were denied a reasonable opportunity to present your case, or material documents relied upon by SBI were not supplied to you, these matters can potentially be raised under Section 34. Merely describing the award as "ex parte", however, is not enough; the record must show that despite your participation/objections you were denied a reasonable opportunity.
Since you say the seat of arbitration is Delhi, the Section 34 challenge would ordinarily have to be brought before the competent court at the seat. The exact court—High Court or the appropriate Commercial Court—depends upon the pecuniary and statutory jurisdiction applicable to that arbitration. The important point is that filing the Section 34 petition in Indore merely because you reside there would ordinarily create a jurisdiction problem if Delhi is indeed the juridical seat.
The Section 34 limitation is also extremely important. Generally, the period runs from the date on which the party making the application received the arbitral award, subject to the statutory provisions regarding a duly delivered signed copy. Therefore, do not wait for execution proceedings before examining limitation. The actual date and manner of delivery of the signed award should be established from the arbitration record and your email/postal records.
A Section 17 interim order and the fact that SBI did not act upon it do not, by themselves, invalidate the final award. The effect of that order has to be examined separately.
As regards execution, the award becomes enforceable under Section 36 subject to the statutory scheme. An objection that the award is invalid because of an improperly constituted tribunal or denial of opportunity is normally something that should be raised through the appropriate Section 34 challenge, rather than waiting for attachment and attempting to convert execution proceedings into a full challenge to the award. Financial hardship can be relevant to seeking appropriate procedural/cost relief, but it does not by itself transfer the Section 34 proceedings from Delhi to Indore.
2. Kotak's criminal complaints in Kolkata
Here, the territorial-jurisdiction objection deserves serious examination. Merely having a branch or office in Kolkata does not, by itself, mean that every offence connected with a credit-card transaction can be tried there. The relevant question is where the ingredients of the alleged offences were committed or where a legally relevant consequence occurred.
For example, the allegations under Sections 316(2) and 318(4) BNS cannot be sustained merely by labelling a credit-card default as criminal breach of trust or cheating. The complaint must contain facts satisfying the ingredients of those offences. In a credit-card dispute, the question whether there was dishonest intention at the inception of the transaction is particularly important for a cheating allegation. Similarly, criminal breach of trust requires the ingredients of entrustment and dishonest misappropriation/conversion; a simple failure to pay a debt does not automatically satisfy those ingredients.
For criminal intimidation under Section 351 BNS, the alleged threatening act and its relevant consequences have to be examined. For criminal conspiracy under Section 61(2), the complaint must disclose the alleged agreement/conspiracy and the role attributed to each accused. The fact that the complainant happens to have an office in Kolkata is not, by itself, a substitute for pleading the ingredients of the offences there.
You can raise the territorial-jurisdiction objection before the Magistrate, but I would first obtain the complete complaint and all annexures. If the summons merely says that an "Offence Copy" is enclosed but the actual complaint/annexures were not supplied, that is an important procedural issue. You should obtain the complete court record and copies before deciding the precise application.
The fact that there are two separate complaints concerning two credit cards does not automatically make them impermissible. Two separate transactions can give rise to separate proceedings. But if the complaints substantially reproduce the same allegations, same evidence and same alleged acts, with no distinct criminal conduct relating to each card, that can be examined as a possible abuse of process or improper duplication. The exact complaints have to be compared rather than assuming that separate case numbers themselves make the proceedings illegal.
At this stage, I would not choose between "jurisdiction objection", "discharge" and "quashing" in the abstract. The first step should be to obtain the complete Kolkata complaint, annexures, cognizance/order taking the case forward, summons and the material relied upon by Kotak. After that, the allegations can be tested ingredient-by-ingredient: territorial jurisdiction, cheating, criminal breach of trust, intimidation and conspiracy.
If the complaint itself does not disclose the necessary ingredients or the Kolkata court lacks the necessary territorial connection, a challenge before the appropriate higher court may become substantially stronger than simply undergoing a lengthy trial. The fact that the underlying dispute is essentially a credit-card repayment dispute is relevant, but it is the actual allegations and supporting material in the complaint—not merely the nature of the underlying debt—that will determine the appropriate remedy.