I think I can answer this question; I am a medium and intuitive and have cleared homes. I also have a background in real estate as well.
If you have an agent, ask them to do the leg work for you, as this is what you're paying them for. Death Certs can be ordered, however you need pertinent info such as date of birth\date of death, full name, drivers license numbers etc. I would check with the mortuary if you can find which one handled the burial and with the prior owners.
That said, IF THE HOUSE IS HAUNTED, (as you have no proof, and it seems that you're wondering if it is without experiencing anything), if you start remodeling then yes, this can stir spirits to come forward.
And the molding paint proves nothing.
If it is a good buy, then I would have it thoroughly checked (inspection, appraisal) and check everything yourself throughout the house (plumbing, water heater, etc.) prior to buying since people who lose homes normally do not have the funds when things break down.
Also, any tax liens that are associated with the home come with the purchase, so have a complete title done prior to closing.
If once you move in, and start work and things start happening, keep a camera close and take pics once you see something. Also keep a recorder on voice activation near the site of the issues occuring. Then contact a paranormal investigative team near your area to come in and check the home.