Coats of Arms - yes this is something I know about. Fairly niche, admittedly.
Meghan had a Coat of Arms designed for her when she married into the Royals. This is par for the course, so did Kate Middleton. Sophie Wessex's father had Arms already. Meghan's father did not require to have Arms awarded for her to get her own.
There is no such thing as a "family coat of arms" or "family crest" whatever the tat shops in tourist areas will have you believe. It doesn't work like that. A coat of Arms is particular to an individual. Some colours/designs/images will appear in coats of arms of people sharing the same surname - so for example the image of a stag's head on a blue background is associated with the McKenzie surname.
Meghan's coat of arms is "impaled" with Harry's on their joint coat of arms. This means smooshing them together on marriage, his on the left with the three lions, Scottish lion rampant, Irish harp, hers with the feathers and white bird thing.
Should Archie apply for a Coat of Arms in the future, the College of Arms would look at his parents' Arms as a starting point for his design. Smooshing together of coats of arms to represent parents and inheritance can get v v complicated and is called quartering.
https://en.wikipedia.org/wiki/Quartering_%28heraldry%29
Loads of people have Coats of Arms and use them on their websites, as do organisations and public bodies. If I had one I'd use it too. I can't blame them for wanting to use theirs. It's impressive to the Americans who don't have the same heraldic system and probably don't realise it's easy enough for anyone to apply for their own coat of arms if they have the money to pay for it.