"I have plans for Saturday."
Translation:Eu tenho planos para sábado.
Though a "compromisso" can be a planned event (an appointment or another sort of commitment) it is not really the same as a plan. Also, if you changed "planos" to "compromissos" I'd guess you would also need to change "para" to "no" (but I'm not a native speaker).
You can use any preposition (para and no), one being "for" and the other "on".
But the rest of your explanation is great.
We use "compromisso" for scheduled things, appointments, dates, anything that will occupy our time and we can't really pass.
You can have plans without having anything settled down yet.
Thank you for the correction. I knew it was dangerous to use English as a guide to Portuguese prepositions: if I make an appointment for Saturday, I then have an appointment on Saturday.