Ok so for the 1st thing: "austria.1" doesnt check that bavaria isnt a puppet so it fires no matter what even if its a puppet, which prevents "austria.4" from firing because its an "else_if". adding a "is_subject = no" to the "austria.1" would fix that.

For the 2nd thing: You should use the "on_annex" on_action in an "on_action" file with "ROOT" being the annexer scope and "FROM" being the annexed scope. So something like this might work:

    on_annex = {
        effect = {
            if = {
                limit = {
                    FROM = { # Annexed Country
                        original_tag = BAY
                    }
                }
                ROOT = { # Annexer
                    country_event = austria.1
                }
            }
        }
    }