I am addressing the one point I know, heraldry.

A terminology note: I would not call it a "coat of arms". A coat of arms has a shield with a design on it, and the design generally conforms to a style of art called "heraldry" that originated in the 1100s in northern France and southern England. (Or so I define it and will defend it.) There is no shield and the curlicues (cursive E R doubled and reflected, with no ordinal?) are not known to any coat of arms I've seen.

This isn't a coat of arms, and British Regiments don't have coats of arms. This appears to be a design based on the Cap Badge of the Grenadier Guards due to the initials in the centre of the badge. (ER twice) For an example, see their website http://www.grengds.com/

A similar hat badge denotes the Household Cavalry Regiment but the initials in the centre of their badge are those of the reigning monarch in simpler format (Currently EIIR).

Thank you all for your replies!