Accomplished and important little self a great burden

Hello everybody.

I have some questions, would you please tell me the answers?

What does as the height of luxury mean?

As the height of luxury, she put down some of her sewing and then found time hang so heavily that she fell to sniping and spoiling her clothes.

I also don't know if sewing means what she was making or the tools of sewing.

But something in the air affected her, and more than once her tranquility was much disturbed, so much so that on one occasion she actually shook poor dear Joanna and told her she was 'a fright'. Amy fared worst of all, for her resources were small, and when her sisters left her to amuse herself, she soon found that accomplished and important little self a great burden. She didn't like dolls,
fairy tales were childish, and one couldn't draw all the time. Tea parties didn't amount to much, neither did picnics, unless very well conducted.

What does shake sb mean in the above?

Does it mean to hit? I read somewhere a sentence like this' if Amey bothers Beth, I will shake her.

And my last question, I try hard but I couldn't figure out 'She soon found that accomplished and important little self a great burden.'

Thanks so much for the help. You are really doing good to me. ??