questions on BRepMesh_IncrementalMesh

(1) If the STP file CAD model is good, I think openCascade should, in turn, give me a good, valid, error-free precise Brep. How do I know if the STP file is good? By reading it into a commercial CAD program called SolidEdge and seeing if it complains or not, and by just visual observation of the model on the screen.

Model validity and interoperability between CAD kernels is a complex matter - there is no simple way to say if STEP file is 'valid' or not. Checking that STEP file is fine in SolidEdge doesn't guarantee that STEP file is valid. Different CAD kernels have different shape validity criteria - for that reason, OCCT STEP translator doesn't just read STEP model, but also applies shape healing to make it closer to OCCT shape validity criteria.

There are 3 points to consider:

1. STEP file format conformance to STEP standard specifications. If model is written incorrectly - than most likely it cannot be read back. However, OCCT reader might tolerate some issues in format. OCCT collects found problems and you may access them to make a log like this for Reading (XSControl_WorkSession::ModelCheckList()) and Translation (Transfer_TransientProcess::CheckList()) steps. Here is an example from CAD Assistant verbose log:

12:49 Count STEP Reader Failures for '1M001934.stp'
       -----    -----------
          22    F:(CONVERSION_BASED_UNIT,NAMED_UNIT,PLANE_ANGLE_UNIT): Parameter n0.1 (dimensions) not an Entity
         137    F:PROPERTY_DEFINITION: Parameter n0.3 (definition) : Entity has illegal type
          Nb Total:159  for 2 items

2. OCCT STEP translator performs automatic shape healing in attempt to fix model to OCCT shape validity criteria. But it doesn't necessarily successes and may corrupt model due to bugs or when it doesn't know how to deal with problems in model. Shape healing failures during translation step are also logged. In addition, you may use ShapeFix tools in OCCT to check model health after STEP translation is completed on result B-Rep shapes.

3. There are Recommended Practices for storing Geometric and Assembly Validation Properties in STEP model. Such validation properties may include volume of solid, for example. If originating CAD system writes such properties into STEP file, you may consider comparing real and validation properties to see if model looks conformant to the model from originating system. Cannot say, however, which systems actually write such validation properties into STEP files.

(6) If all this is true, I should get a a bunch of Triangles for each Face. The Triangle Vertices along the shared Edges should geometrically coincide perfectly. Which in turn means that I can produce a topologically water-tight polyhedron by merging these common boundary Vertices. And this merging operation should be quite robust, since I can set the Vertex merging tolerance to a very small number. Also, as stated in point (4), this should be true regardless of linear and angular tolerance setting. The polyhedron may be a terrible approximation of the model, but it should still be topologically water-tight. Is that true?

In general, your considerations about water-tight mesh generation looks correct. If input B-Rep model is a valid closed Solid shape - then BRepMesh is expected to generate a water-tight mesh on success. It doesn't validate water-tightness of result on its own, though. You might need to perform some mesh quality checks if this property is critical to your application.

Note that algorithm may generate some warnings/errors reported through BRepMesh_IncrementalMesh::GetStatusFlags() as IMeshData_Status mask - make sure to check them as a first step. And of course, you may also struggle into some BRepMesh bugs leading to mesh quality issues.

Hard to understand why a 2D Delaunay triangulation would fail by just changing this number.

Consider sharing some models that doesn't work for you and meshing parameters. You may try to weed out a smaller solid from complex model.

(2) Is 2D Delaunay triangle meshing the only technique available?

You may try Delabella algorithm within IMeshTools_Parameters::MeshAlgo parameters for building initial 2D tessellation. But I don't think that it will draw a considerable difference on your issues - most likely the reason is located in another place (like handling tiny edges, self-intersections and similar tricky issues).

If you pass 10 as angular deflection it may be incorrect as it is treated as radians.
For shape validity checking you may use BRepCheck_Shape class.