Without considering all of the possibilities right now, I'd be inclined
to call the city (or county?) building dept. to find out what complaints
they have heard and what the expected soil conditions would be after 10
inches of rain. You may just have a situation with the soil being
completely saturated and some of the water found a weak point to exit.
I'd also leave the hole in the concrete alone for now to monitor.

You've stated there is a slope, but not where you are in relation to the
bottom of the slope or what type of drainage system there is to drain
storm water from the property. Lots of info that may have a bearing is
missing.