Arthur often walks with both arms swinging forward and backwards in unison which is unusual. A "normal" walking gait is left arm swings forward at the same time the right leg goes forward, etc.
Yes, so glad to see you see that Tommy has a sense he won't survive the assassination... and his responses with both women line up with this. since he's going to die, he can have fun with May who he knows is attracted to him. But then in his quieter moments, his fears of dying lead him to reach out to Grace. 2 very human responses that don't contradict each other at all, I think....