Buying a House On Underground Spring. What to do?
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 &amp; 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!