Learn English – Difference between “I don’t mind” and “I don’t care”

The full name of the document is Last Will and Testament. One definition:

A document in which a person specifies the method to be applied in the management and distribution of his estate after his death.

Will is a common term to refer to this document. I wouldn't call it informal; I think it's what people use most of the time. In a legal context you're probably better off using the full name, though.

Comparing these two definitions from OxfordDictionaries shows the two words obviously overlap...

embarrass - cause (someone) to feel awkward, self-conscious, or ashamed
ashamed - embarrassed or guilty because of one’s actions, characteristics, or associations

But two key differences are...

1: embarrassed more often applies to socially awkward contexts, rather than regret, guilt
2: You don't usually feel embarrassed when you're alone

I don't really like OP's idea that being ashamed is more "serious" than being embarrassed. I might feel ashamed if I discovered I was the only person in my road who didn't leave a Christmas tip for the postie, but that would be nothing compared to how embarrassed I'd feel if I discovered said postie knew exactly what was in all the packages she'd delivered over the preceding year!

TL;DR: Shame is mainly a response to having transgressed your own (internal) moral code. Embarrassment is more about feeling that others may laugh or look down on you for something you did.