[planede]

1. It's not intuitive that you can type in a dropdown.

2. It's not always obvious if a dropdown is focused or not.

It's orthogonal, but focus doesn't always cycle in the obvious order of input fields with nothing in between.

As for the field, couldn't it be a text field with a small down arrow within for a dropdown option?

[Etheryte]

Every native dropdown in your OS supports typing to select an option. While it might be arguable if it's intuitive, it definitely is a common pattern.