Corrections in red.  Stylistics in blue.

Task 1

Write a text. Words to use: to lead, to separate, to engage, engaged, strained, to make one's appearance, to fulfill, comply with, rate, rapid, rapidly, to get lost, beverage, invitation.

This invitation was her only opportunity to separate herself from all her past life. So Eva decided not to miss this exclusive chance. The girl dressed in a glamorous red dress which complied with her mood, and made her appearance at the annual party in the Mr. Smith's mansion. Firstly, Eva looked/appeared strained, and tried not to get lost while surrounded by young and aged men and women in bright attires, and waiters offering a wide range of beverages. But rapidly she had got used to the situation, and 15 minutes later she'd already been around the circle of people, who at every moment were ready to fulfill every desire of this woman. At a rapid rate she engaged a lot of young lads. This night she was a sparkling lady, whose charm lead everyone for she around the luxurious garden. [1] And as a result of this evening, she became engaged with a rich, young man from California.

[1]  This sentence was hard to understand.  If you think I misunderstood the sentence, please paraphrase in English or write the sentence in Russian, and I'll try again to help.