First of all, welcome aboard!
To answer your question: From the pictures neither the boots nor the ankles look broken to me.
The little ball joints that are stuck inside the boots just need to snap into the ankle piece that you are showing in your picture; so that's correct.
It happens quite often, that one - or even both - of the shoes of a figure arrive unattached. Happened to me a few times with various manufacturers. That's not really an issue.
What I can't tell just from the pictures is if the ball joints properly fit into the ankle sockets...
Sometimes the ball is a little too small and thus the shoes keep falling off and other times the ball is a little too big and you have a hard time popping them back into the socket.
Just give it another try and make sure the ball joint stays in the middle when you do. In your picture you can see that the joint of the left shoe tilted forward... maybe that's why it didn't work. They tend to wobble around when you try to push them into the ankles.
Hope that helps.