Yes, you can. 'Very' intensifies 'proud' and 'so' intensifies 'very'.

You have to choose between so and very. They both have the same meaning.

Of course.

Hi, Aanya! This is okay if you're speaking in an informal way. However, it's better to use "I'm so proud of you" or "I'm very proud of you"(formal). This is because "so" and "very" share the same meaning, so combining them both in one sentence is repetitive. Hope this helps! 😊