Meaning Difference – ‘I am Done’ vs ‘I am Through’

Get through means "to suffer through."
To get through something usually means in an emotional state, like to get through a divorce, or to get through something challenging, like a test.

She was so tired that it was difficult to get through the day.

Go through means "to pass through something."
"Go through something" is the physical of "go through something," and it is always in the present tense, like "go through a divorce" or "go through a tunnel."

After you buy your token, put it in the slot and go through the turnstile. Go through the old city gates and you will see beautiful 15th century church.

So its always you go through a door, not get through a door.

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.