To answer your questions, refer to the following Workbench figure.

Your understanding is wrong. Nastran SOL103 is what Ansys calls Modal and is also called Normal Modes or Eigenvalue analysis.

Nastran SOL111 can do Random Vibration and Harmonic Response. One of the cards used is EIGRL which requests the Modal analysis.

In ANSYS, you put a Modal analysis upstream and link the Solution cell of Modal to either a Harmonic Response or a Random Vibration analysis Setup cell.