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In this question, I couldn't reconcile with the answer.

1. Step 3 is slowest
2. So rate law = k [NO+] [ NH3]
3. But we cannot have a rate law in terms of intermediates
4. NH3 is intermediate. So per rate law of step 2, R = k[NH4+]
5. So overall rate law is R = k[NO+] [NH4+]

Please explain the logic of your answer and where am I wrong

Overall reaction is
HNO₂ + NH₄⁺ ...> 2H₂O +N₂
Rate law for step I
Rate = k[HNO₂][H⁺]
Rate law for step 2
Rate = k[NH₄⁺]
step 3
Rate =k[NO⁺][NH₃]
This step is rate law determining step and you need to remove intermediate by  reactants from which these intermediates are formed.
Replace NO+ by HNO₂ and H⁺
Replace NH₃ by NH₄⁺
Here H⁺  is the catalyst.