I was happy, because I woke up at 8:00 recently.

If 8 AM has been your typical (habitual) time to wake up, it is better if you say: I was happy, because I've been waking up at 8:00 recently.

After that, I studied.

Another alternative to "after that" is "afterwards"

AIn the afternoon, I called a /my friend.

During [time period of day] = in the morning/afternoon/evening/night time

You could say "a friend" or "my friend" but not both

She wais so funny.

You would say that she IS funny, as if it is a personality trait (that is still true now that you are off the phone).
But if you wanted to insist that she was very funny during this phone call specifically, you could say, "She was so funny on the phone" or even, "She was so funny today."