Congrats on your pending venture, a new home!
I am a certified Home Inspector and have a few ideas for you.
Actually, there are several items that a good home inspector is going to look at that are not on your list. Keep in mind that an inspector is going to be able to render an opinion on the condition of the systems and structure of the house. Other items should include, chimneys, flashings, gutters, windows, screens, sills, exterior fixtures/lighting, attics, vent fans, proper wiring, GFIs, water heater/temp, heating systems, fireplace dampers, window operation, door operation and weather stripping, step and railing safety, and the list goes on. Extra inspections may include, radon, water, septic systems, wells,or pools.
If you want a good reference and sample checklists, I recommend the book The Complete Book of Home Inspection by Norman Becker, PE. There are several good books out there, but this one is simple and to the point.
When you do find a property that you want to make an offer on, be absolutely sure you include a contingency, or condition of sale, that calls for a professional home inspection, and that the inspection results meet with your approval. In other words, if any discrepancies or findings are in the report, you can get your deposit back and walk, or negotiate with the owner for a reduction in the amount of your offer to professionally repair the problems.
The average cost of an inspection in my area for a home under 4000Sq feet and less than 100 years old is about $350.00. Under no circumstances should you not have a professional inspection and the associated contingencies in your offer to purchase. Once you make an offer, a DIY inspection is not legally enforceable, and you will have no recourse and unable to walk away with a refund of your earnest money deposit.
The sump pail is there precisely because you can't prevent water from coming in, at least under the slab. It's unclear whether your home has foundation waterproofing installed.
It's also unclear why two sumps couldn't keep up. In all but the worst scenarios, one pump should be adequate, and it should only run every few minutes at most. If you have pumps running constantly due to moderate rainfall, you have bigger concerns. Is the landscaping around your home sloped the wrong way? Does your neighborhood's topography result in heavy flow through your yard? Is your home located in a lake or pond?
I do appreciate that you thought to mention the makeup of your ceiling. That successfully conveyed the scope of your problem. Unfortunately, a sump pump won't help if the water gets that deep.
Best Answer
Looks like a pretty small stain. Even if the wastewater pipe is the cause I don't think it would be a big deal to fix. The risk looks pretty small to me.