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The goal of nonlinear contact (not bonded) is that the parts should not penetrate by an excessive amount. Insert a Contact Tool into the Solution branch then Insert a Penetration plot into the Contact Tool folder to evaluate the magnitude of the penetration on a contour plot.

1)   Updating normal stiffness in each iteration.

This is generally the best setting, because it allows contacts that have excessive penetration to automatically adjust the stiffness to reduce the penetration. There is a computational cost to do this, so when you don't need it, you can turn it off to get a very slight improvement in solution time. You can't just set the contact to an extremely high normal stiffness because that causes numerical problems for the solver and the solution may not converge.

2)   Detection Method:

The results are different between Nodal-Normal-Target method and 4 other options.

There are choices because there are differences in the computational cost of each option. The default option provides the fastest solution time, but if you observe excessive penetration in the results, you can change to another option to reduce the penetration and incur a slight increase in solution time.

3)  Interface Treatment:

Adjust to Touch is automatically selecting a value to put into the Offset setting, which results in the contact being closed. This is useful when the CAD geometry is perfectly tangent (and also when it is not perfect), but due to discretization in meshing, a tiny gap has been created. The solver has a very difficult task getting started when contacts are initially open, and a much easier task when the contacts are initially closed.

It's always best to have the CAD match reality as close as possible, but Offset can be a time saver to eliminate doing a very small adjustment in CAD and allow an interference to be created where none existed in the CAD geometry. For example a press fit of a shaft in a hole, where both the shaft and hole were drawn at the same nominal diameter of 10 mm, but the tolerances on the parts call out an interference fit. You can just type in the magnitude of the interference in the offset parameter in the contact definition.