1)Why in Islam girls cannot go out alone , but here in Europe is it possible to go out alone ?2)What is the problem when girl has a boyfriend, before they get married?3)What are the problems bad effects of freedom of Europe on and American women (Like sex,bad clothes, etc.)4) Men in Islam can have many wives, why can't women have many husbands?Please I want full answers .5)How can I invite non-Muslim people to be Muslims?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is unlawful for the woman to travel alone without a Mahram (a non-marriageable man (brother, father, uncle etc.). This prohibition is due to the fact that a woman traveling without Mahram can encounter a lot of difficulties, including being raped or tempted to commit Haram acts.
It is lawful for the woman to leave her house for some need provided she is certain that she will not be tempted or her going out will not cause her some misfortune.
So, she can go alone to schools, hospitals or to any other place if there is a legal purpose for going there and provided she respects all the Shari'a conditions related to this.
For the Fatwa about boyfriends and fiancé, please read 81356.
There are many bad consequences that result from libertinism of women. These include sexual anarchy, mixing up progenity, spreading sexually transmitted diseases, etc.
We do not call this freedom, it is rather worshipping Satan and being inclined to his whispers. It also makes real the bad ideas of the ill-informed people who take every opportunity to influence women by beautifying to them to perform bad acts and calling that freedom.
For your fourth question read Fatwa 83644.
For your 5th question read this Fatwa 82520.
Allah knows best.