I found pyeuclid to be a great simple general purpose euclidean math package. Though the library may not contain exactly the problems that you mentioned, its infrastructure is good enough to make it easy to write these on your own.
I really want a good answer to this question, and the ones above left me dissatisfied. However, I just came across pythonocc which looks great, apart from lacking good docs and still having some trouble with installation (not yet pypi compatible). The last update was 4 days ago (June 19th, 2011). It wraps OpenCascade which has a ton of geometry and modeling functionality. From the pythonocc website:
pythonOCC is a 3D CAD/CAE/PLM development framework for the Python programming language. It provides features such as advanced topological and geometrical operations, data exchange (STEP, IGES, STL import/export), 2D and 3D meshing, rigid body simulation, parametric modeling.
[EDIT: I've now downloaded pythonocc and began working through some of the examples]
I believe it can perform all of the tasks mentioned, but I found it to be unintuitive to use. It is created almost entirely from SWIG wrappers, and as a result, introspection of the commands becomes difficult.
You may be interested in Python module SpaceFuncs from OpenOpt project, http://openopt.org
SpaceFuncs is tool for 2D, 3D, N-dimensional geometric modeling with possibilities of parametrized calculations, numerical optimization and solving systems of geometrical equations
Python Wild Magic is another SWIG wrapped code. It is however a gaming library, but you could manipulate the SWIG library file to exclude any undesired graphics stuff from the Python API.