To answer your first question, the Torah is very clear that interest may not be charged to Jews, but may be charged to non-Jews:
לַנָּכְרִי תַשּׁיךְ, וּלְאָחִיךָ לֹא תַשּׁיךְ--לְמַעַן יְבָרֶכְךָ יְהוָה אֱלֹהֶיךָ, בְּכֹל מִשְׁלַח יָדֶךָ, עַל-הָאָרֶץ, אֲשֶׁר-אַתָּה בָא-שָׁמָּה לְרִשְׁתָּהּ.
Unto a foreigner thou mayest lend upon interest; but unto thy brother thou shalt not lend upon interest; that the LORD thy God may bless thee in all that thou puttest thy hand unto, in the land whither thou goest in to possess it.
So this practice goes all the way back to the giving of the Torah. As opposed to (e.g.) Islam's view, Judaism does not really consider charging interest to be an immoral act. Lending money is a service, and there is nothing wrong in general with collecting payment for such a service.
The answer to your second question depends on who is doing the lending. The prohibition of interest applies equally to the lender and to the borrower; however, this again only applies when a Jew is lending money to another Jew. It is completely normal for Jews to take out an interest-bearing mortgage from a bank in order to buy a house.
It should be noted that the verse in the Torah seems to be talking about the case of lending money to a poor person who desperately needs the money. While the law also applies in other cases, the rabbinic literature is more lenient about cases where the borrower does not need the money to survive (e.g. a business investment) and allows certain loopholes that fulfill the same purpose as charging interest. For more information on that, research heter iska (See: How is a heter iska made to work with a non-business loan? and How do Interest Loans work in Israel?).