You didn't indicate your location or site characteristics (slope, hillside, etc), but the location of the country, even generally could be helpful, but not required.
You indicated the water bill was not high, so it could not be a water leak. That would only be if the leak was after the meter. However, the leak could be before the meter and impossible to detect through usage alone. A few tests to help determine if this is a spring:
Temperature: Spring water would be the average annual temperature (between 56-59°F). If it is different, turn on the cold tap water and measure it's temperature. If it is close to the temp of the water in the sump, that is more likely the source. If the water is a different temperature than either of those, it is likely ground water.
Chemical Composition: Have the water chemistries evaluated and compared to the houses tap water - if they are very similar, the water is likely a leak from the main, and not a spring. If there is chlorine, that is a dead give-a-way (but it off gasses quickly, so absence is not a complete indication)
If it is, in fact a natural source, then if could be spring or runoff. Most springs are intermittent to some degree with natural cycles. Perhaps this is a heavier time or from recent storms that are working their way underground and bumping into an impervious layer of shale that your house was built on top of. As a home buyer, you only have a point in time reference, and the neighbors may not know the details from the inside of the house as to how often and consistently the pump runs.
You also assumed it is only pumping a few gallons — some sumps hold 15-25 gallons. If it were built intended to handle the flow you mentioned (~900 gal/day) it likely would have been larger to begin with to run less often.
Is this a red flag / deal breaker? Is this just something we need to
keep an eye on, or is there a possibility that the foundation might
crumble at any time?
If it has been in place for 25 years, I don't think this is a major concern. If it was retrofitted, especially recently, I might have a different opinion. But this depends on where you live somewhat — is your area composed of a lot of Karst or cave features? Florida for instance is known for its sinkholes and springs are one possible concern with those.
In most areas, however, if the water is directed well, this should not be a concern because the water is directed away from the foundations and out of the house properly. Consider getting a home inspection & point out your concerns. They may find additional evidence of water damage, remodeling or other evidence of concerns that you could have overlooked.
Assuming it is not critical, what precautions should I take? I
already plan on buying a water-powered sump pump as backup, and
getting a couple alarms for both pumps. The current pump already has
a battery backup.
Alarms and backups are great. A small, but high-quality generator would be fantastic to keep things running for a longer period if needed. Make sure it's rated for constant duty. Be sure to have a plan to allow easy switching from the pump's current electric source to the generator. You could make this tie-in at the panel or the pump, but be careful not to backfeed into your system.
The water looks clear and fresh. What can I do with all this water?
Anything productive?
Do you have gardens? Make a rain-barrel type system using large holding tanks - plus, you'll see how much water you are actually removing seasonally. But be careful in planning that whatever you do that your system is able to handle cold weather without freezing up or you risk a damp basement and a blown pump.
But If you really are pumping what you claim (3 gal every 5 min = 960 gal per day) you will likely have limited use for all that water, unless you're in California and will share with your neighbors!
Good luck with the new home!
I have experienced massive water flow in the sumps when they've been unplugged or just not running while water continues to build up around the foundation. If you have a lot of clean #57 stone around the footer, under the slab, and even up the exterior walls some, it will "store" water in the voids between the stone. This water can travel quickly to the sump when it is "stored" between the stone in this situation, which is precisely why the stone is used in the first place. Sand will do the same thing, but slower.
In torrential rains, you need to move a lot of water fast... and clean #57 or larger stone allows you to do that. Basically, the stone is a big pipe or conduit.... and water can travel both horizontally and vertically through it, so long as it's not infiltrated with sediment.
Is the "every 12 seconds" you speak of measured just after you plug in the sump? Depending on how much 4" pipe you have around your foundation, a gigantic amount of water can be stored in it. Eventually, though, the pump will "catch up" and all that stored water will be gone. Then I would expect that it slows back down to a more reasonable rate...even if it's still raining outside.
The time to be most worried is when the sump ISNT working. That's when you start to get differential settlement and buckling walls in freeze-prone areas.
Best Answer
I would second the comments recommending a second opinion. A sump is in the basement to allow water to be drained away if it accumulates around the footings. If there's no water there it quite probably means that your water table is low enough that there's not seepage. It also would indicate that you have decent drainage around the house and rain water is running away and not down along the foundation walls.
Even if there is a blockage in your sump I would expect there to be some water in the bottom if you currently have a water problem. Blockages often involve crushed weeping tile or other drainage pipes. However, it would not usually be a complete blockage and if you have a have water on the outside trying to get in at least some of it should be seeping into your sump even through damaged draining lines.