Hi,
I can answer question 1, and I will defer to Stein’s answer for 2 and 3. The “Catenary solve unsuccessful” warnings from MoorDyn simply mean that an analytical solution could not be found for the catenary line shape. MoorDyn then tries to solve for equilibrium by holding all coupled points static and letting the line ‘fall’ into place. In your case, after 19.75 sections the fairlead tensions converged for each line indicating that the line had reached an equilibrium position. This will not affect your results and means the simulation is starting with the line in the correct position.
This initial condition solver is controlled by the flags TmaxIC, dtIC, CdScaleIC, and threshIC in the options section of the MoorDyn input file. You can read more here: Input Files — MoorDyn 2.1.0 documentation
Ryan