Dodgy parameters?

I think your gut is right.

Mudstone, and most rocks are typically designed as drained materials. Provided the material is jointed, you can use the Hoek Brown criteria to calculate drained parameters. For a mudstone, id guess something like phi of 28 degrees, c' 50-100kPa. Thats a big shot from the hip, fracture spacing, rock strength etc all play a big part. If its limited fractures and high strength, you will get much higher parameters that I suggested. Also, with those parameters, you are getting very little lateral pressure from the rock, as expected.

The 'running sand' parameters are unusual for me, I have never seen anyone assess it like that. I see what they are trying to do (i think). They think the running sand will behave just like water so they have essentially analyzing it as if it was water with unit weight of 9. Running sands only run if they have somewhere to run too. If you are designing a sheet pile wall or some other wall type that restrains the sand they I woudl just be designing it as typical with an earth pressure calculated based on a realistic phi value.

Bedrock gualt clay, would typically be a Claystone. Same comment as weathered mudstone applies.

I find it unusual to get a layer of running Sand between two rocks....

As a general response, I wouldnt be thinking about clays being Phi of low 20s and cohesion. London Clay is probably 22 degrees, c' wouldnt be considered for the majority of design work. Irish Glacial Till has a phi of 34 degrees and zero c'. Its all about geology and stress history