I think the best resource is to find out what other comparable homes in the area you are considering purchasing have listed and sold for. It is best to review recent home transactions. Then from there you can make an educated offer on a property. This will help you from over paying for a property. There is no set limit on how little below asking price you can offer on a home. But, ultimately it will be the owners decision on how much they are willing to accept. You may want to be cautious when bidding though because Sellers do sometimes become insulted if an offer is very low and may not want to deal with the Buyer. I guess the best suggestion is to make an educated & fair offer for the property. Try and work with the Seller to come to a reasonable price you both feel comfortable with. As far as how long a house has been on the market your Realtor can tell you that it reflects as DOM on the listing sheet. But, make sure they run a history report to see if the home was on with another realtor prior to the current broker. Finding the best deal coincides with finding an experianced intelligent realtor to help guide you through the homebuying process. Work with a Buyers Agent.
If you are working directly with a real estate professionak, he/she will walk you through the process. Agents understand the business and know how to best support their customers.
Sounds like you are going solo.......
Good luck, it could be a rough trip alone.