#1 would read more smoothly if you start combining sentences so you don't have so many short, simple sentences in succession. Like this:
Marie Curie was a French physicist who was born in Poland. She discovered pure radium, and she is the only person to have ever been awarded two Nobel Prizes.
#2 The sentence is correct, and your placement of the period before the closing quotation marks is also correct.
1. She is Marie Curie. She is a French physicist. However, she was born in Poland. She discovered the pure radium. She was awarded two Nobel Prizes. [She was the only person to be awarded two Nobel Prizes.]
(Would you like to check the passages above? Check them please.)
2. He discovered "the Law of Universal Gravitation" and "the Three Laws of Motion." [Motion".]
(Is this passage corect? What is the correct position of period?)
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