1) A negligible amount of penetration is problem specific. If the diameter of the pipe is 3 meters, then 0.3 mm may be considered negligible. On the other hand, for a pipe with a diameter of 3 mm, 0.3 mm would be a huge amount of penetration. In the domain of optics, for a 1 meter mirror, a 0.1 mm penetration would be huge. An acceptable penetration may be on the order of 1e-6 mm.
2) Quadratic elements can capture curvature, but are not the only consideration. The first consideration is to have the nodes on each side of the interface line up. That will allow a linear mesh to behave well with the contact elements. Using a grossly exaggerated example so you can see the effect, these two circles were meshed with 6 linear elements around. The first mesh has a clearance when the mesh is lined up but has an interference when the mesh doesn't line up. Quadratic elements can help this, but linear elements tend to have fewer problems with convergence in contact models.
3) Inflation can help to get accurate stress near the surface.
4) Contact Match is great when it works, but sometimes it is simpler to just use sizing controls (number of divisions) on edges and splitting the body to make sure two circles start and end at the same point.
5) If the contours are smooth, that is a good indication of a quality mesh.