But you can use facebook api or the Construct facebook plugin and IG together in your game, and have facebook plugin when a button is clicked to wall post something to user profile, and IG do his gaming platform thing(which isn't much that C2IG API does outside a leaderboard call, some profile info, and a few share/invite to app of friends chatbot, ads, and kinda that is it, you should look at the Instant Games plugin description in the manual to see what features are available and not.)
No, that is not possible and also not allowed by Facebook.
There is a ShareAsync function in the IG SDK. It works fine in this plugin. Just make sure you have the image on the layout.
(The funtion can be used to post to your own wall, depending on the device you are plying on. But mostly it is only to send to messenger friends. But this is nothing you can decide, it depends on the device and os, and it can change..)