Question

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?)

Answer 1

#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.