Learn English – ‘Feel embarrassed or feel embarrassment’

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.

It depends on a context. They both may mean the same thing in example like this -

He can hardly write = He can barely write

But then, if you check all the meanings for both the words, you may come up with an example where the words cannot be interchanged.

Now, when in case where hardly refers to 'almost never', replacing it with barely may not sound natural.

"I hardly go for a social gathering" over "I barely go for..."

Edit after the question is edited:

Yes, I agree with djechilin (+1), use poorly or badly instead. The book is poorly translated.