Bluebird Minion Questions

[Madamepancake]

So I think the bluebird is really cute but I would like a few answers before I go and get one. (This also applies to the opo-opo and nutkin if anyone knows)

1. Does it really respond to the /beckon emote? (I've seen cases where it doesn't respond, but they were very old posts)
2. If I sit down or fish, will it sit on my shoulder too after the emote?
3. Does it do anything else?
4. Can I run and have it continue to sit on my shoulder or will it fly off?

Thanks in advance If anyone had a video of the interactions and would like to post it, that would be even more amazing!

Edit: Thank you so much for answering!!!