You’ll have to ask the developer regarding point (3).
As things stand, on your system you are successfully connecting to wired (eth0), so connman will not try to connect to wlan0 automatically. (The file /etc/connman.conf contains the line PreferredTechnologies=ethernet,wifi to prefer ethernet over wifi.) There is a description of how it works at https://01.org/connman/documentation.
You can still try a few things:
In connmanctl make sure that autoconnect is true for the wifi interface. (Type help in connmanctl for more information.)
If that doesn’t work, a simple shell script running the connmanctl connect wifi_xxxxxx_managed_psk command might also work.
Edit: Please also look at this post: Network Config: two networks - #7 by JimKnopf