1. Sodam Park is a very important place for me and many others.

2. I often visit the park for family picnics.
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Q1: What does 'for me and many others' modify? What is the part of speech of it?
Q2: What does 'for family picnics' modify? What is the part of speech of it? An adjective phrase or adverbial phrase?

1 - it's an adjective modifying place.

2 - it's an adverb modifying visit.