I recently bough a gambrel roof home in Topanga, CA where I will get about two weeks of heavy rain in Jan/Feb and then fairly dry the rest of the year. The house is seated into a hill with the front half exposed (stucco) and the rear half of the house is backfilled the full height of the basement.

The house has no rain gutters and has a ~3ft sidewalk and then retaining wall separating the negative slope of the hill and the house. The garage has a water leak and as I began digging in the area (I'm about 4 ft. down) I see that they just backfilled over the stucco and then put a rubber barrier up to prevent leaks. It looks like the top of the barrier was also below grade so seemingly water was just pouring down between the barrier and the stucco with no drain-tile below.

A few questions:

1. How do I know if I'm dealing with a ground water leak OR a runoff leak? Given that they didn't put a barrier high enough and there are cracks I'm assuming its a runoff issue BUT I don't want to go through all of this trouble and miss the actual problem.

2. Is stucco below grade acceptable or am I asking for trouble? If its trouble is the fix to break up the entire concrete sidewalk and dig down to the base of the concrete foundation? In some areas that would be ~10 ft so I'd love to avoid this if possible given that I'm doing it by hand and there is no way to get a machine in based off of the terrain and my checkbook. I also don't want to ignore this and have my house crumble due to water damage.

My gut tells me that installing rain gutters to direct water away from the foundation (its coming full speed off the steep roof) and has inadequate grade to drain away from the house AND sealing/putting a new barrier in where the leak is will solve my issue but I don't want to overlook additional possibilities.