We can understand your frustration and empathise with you. It is true that lending firms do not decrease rates automatically for existing borrowers when they start offering lower interest rates for new borrowers. It is also true that they charge a conversion fee for granting lower interest rates. This is irrespective of whether it is a bank or Non-Banking Finance Company (NBFC).
While some say that their conversion fee is a one-time charge, there are others who charge every time you want interest rates lowered. They do increase interest rates automatically when interest rates rise. Details about this will be mentioned in your loan agreement. If you are not happy with your Home Lona provider, you can consider a balance transfer. But do check the terms regarding the processing fee, conversion fee, and other charges before you do.
In case of prepayments, lenders should allow you to choose between reducing your EMI or your tenure. You can insist on having a lower EMI after your prepayment. We suggest that you talk to your bank about it.