1. You should use a sampling frequency of at least 20 times 26 Hz. What is the frequency of mode 2? If the sampling frequency is too low, you can have errors. When the sampling frequency is higher than necessary, you are only wasting time. You should increase the sampling frequency until the results stop changing. This is like the Mesh Refinement Study concept. Make the elements smaller until the stress result stops changing.
2. Yes damping is very complicated. It is further complicated because some types of damping are available in one analysis type and not in another type: for example MSUP Transient vs. Full Transient.
How are different damping coefficients different? That goes back to the equations of motion being formulated by the solver and where the damping term appears in those equations. The ANSYS Damping pdf is helpful, but not completely clear.
If you are doing Full Transient, there is no Modal. If you are doing MSUP Transient, the Modal should be undamped. The damping is applied in the MSUP Transient either as Material Damping or under the Damping Controls in the Analysis settings.