I make at least two offers on a property. One, an all cash offer won’t be affected by the balance or the note, because it’ll be 70% of Full Market Value (FMV) minus the repairs. If you owe more than that, you probably won’t sell it to me (some do, however to avoid foreclosure).

I’ll make you a FULL PRICE offer if you’ll keep your existing financing in place while I get one of my buyers qualified to refinance and cash you out. In that case I need to know the monthly payment in order to see if I can even get enough from my buyer monthly to cover the note. ARMs and other bad loans make that difficult sometimes. In those cases the seller may be willing to continue paying a portion of the payment until the refinance occurs. They’d prefer to pay $500/ mo instead of the $1800/mo they now pay.

It always depends on the seller’s motivations.

HTH
References :
Me. Real Estate Investor. http://www.red12.net

1. You have a house on the market
2. A real estate company is interested in purchasing this house
3. They want to know what your payments are

Your questions
1. Why would they want to know your monthly payments

They may be interested in leasing the house back to you as you wait and search for a replacement property (if this is the case). They’ld probably then try to lease it to you at an amount close to your current payments. They may want to figure out your outstanding loan and make an offer to match just the loan if you are a distressed seller. I cannot think of any other reasons.

2. Can they find out how much you owe on the house?

They can search public tax records and find out what the last sale was. I do not think they can find your outstanding loans without running a credit check.
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