While having a conversation about someone, can I say "saw him yesterday" instead of "I saw him yesterday"?
The 'I' would be implied so you could use it. However, omitting the 'I' can make the sentence sound flippant in certain contexts and even rude occasionally.
If your friend asked you "Have you seen Jim recently?" and you said "Yeah, saw him yesterday" that would be fine but for more formal conversations, or for writing, I would keep the 'I'.