I applied my wife’s dependent visa using my bank statements and giving a sponsorship letter. Didn’t have such issues.

This is one of the easiest visas to apply if you meet requirements. It's total waste of money to hire an agent for this. Spend a couple of hours and search this group about your doubts, you'll have all answers.

On New Delhi embassy's website it doesn't mention that foreigners cant apply but still it's better to email embassy and confirm. Most likely you should be good to submit your Indian entry stamp, visa copy and hotel booking as proof of legal stay. Once you submit application, you will get a receipt with embassy's bank details. You can go to any "DBS Bank" branch and deposit the fee in cash and then email the deposit slip to embassy.

Advice for you, look up info before posting misinformation!

Check your consulate's website about processing times + add 1 week for delays/additional document requests.

Yes, just carry both passports.

Which embassy did you apply at?

What's your nationality?

Just printed DTV. How long did it take you to get it?

Based on recent approvals, hanoi seems to be fastest and not so complicated.