Beardie arm waves are typically a sign of submission. It's saying to you, "I'm little and harmless, please be kind to me!" Another common behavior is bobbing it's head, which means, "I'm tough and I mean business!" Arm waving is usually attributed to females, and head bobbing to males, so people see their beardie waving it's arms and assume it's a girl. This isn't usually the case. Although it's true when put together a female will usually wave to a bobbing male, both sexes are known to use both behaviors, and it's really just their way of establishing who is boss.
As for color change, it's most commonly due to temperature or mood and is nothing to worry about. Here are two pictures of the same dragon taken on the same day. As you can see the difference can be quite dramatic.
warm and cozy inside his cage
wet and cold after an outdoor shower
-----
2.0 bearded dragons (Ocho / Domo-kun)
0.1 kingsnake (Rio)
1.0 ferret (Playstation)
1.0 cat (Wally)
0.1 dog (Tima)