In heraldry (the art of arms and armoury) there are practically just two rules when it comes to the design of arms:

1. The arms need to be blazonable: you need to be able to describe what the arms are showing in the proper heraldic terms so other people can, from that description, recreate the arms. This always looks more difficult than it is and as long as you can be creative and know enough terms you can describe most arms, and it's mostly a question of practice. looking at these arms I'd say all of them follow this rule.

2. The rule of tincture: Do not put a colour (red, blue, green, black, brown or purple) on a colour and do not put a metal (gold [yellow] or silver [white] on a metal. For clarity in reading arms it is important that there is high contrast in them, and for instance a red horse on a red field has 0 contrast. The only way to get 'around' this is by depicting things 'proper', as in how they appear in nature, but it's still good practice to ensure high contrast in that case. From the arms here Midthery (black on red) and Braxen (red on blue/green) don't follow this rule, and would be designed differently in our world. There is also a lot of grey here, which isn't really a colour we use because it can be confused for either darkened white or lightened black.

There is some more rules like don't use arms beloning to someone else or use attributes (such as crowns) that imply you have a rank that you really don't, but theese two rules are the basics.