For the captain, the AI appears to decide based on the Influence attribute, the players reputation and the players age (an older player with lower influence will take prescient over a younger one)
I tend to assign my own captain as I like it to be a defender or midfielder who is a first team regular, and I decide it based on Influence which you can see. I have no idea if it makes any difference, but it makes me happy.
I also set the freekicks based on the Set Piece attribute, but only to a player who has over 15 for this, otherwise I let it default
Penalties I let default, unless I have a player on a hat-trick, or a player looking for some goal scoring record or highest scorer award at the end of the season.
The artist formally known as The Eejit