1. how do we know which prepositions are added to certain nouns? is there a systematic rule? is there a rule explaining why the noun access goes with the preposition to ? thank you
I don't think there is an easy-to-learn rule. For instance, if you look at expressions of emotion, you find a variety of prepositions after the noun:
1. I'm in love with Miss Q.
2. I feel some sympathy for Miss Q.
3. I feel only hatred towards Miss Q.
To complicate matters still further, you could use "towards" in #2, and "for" in #3.
But you will eventually become accustomed to the different combinations, if you continue to read widely in English.
Not a professional ESL teacher.