Repentance, prayer and giving of charity are 3 basic ingredients of atoning for ones sins.
In sins between man and his fellow man, one must ask for forgiveness and receive it from the person he wronged before he is able to qualify for atonement.
Jews atone for their mistakes the same way that they've done whenever there wasn't the Temple. The individual strives to never repeat their mistake, they pray to HaShem (The Creator), they ask...
The sacrifices only ended because the temple fell; the Romans destroyed it in AD 70. Sacrifices cannot be offered anywhere else. Also, in Judaism the sacrifices were only ever for unintentional sins...
The term "sin" is generally not used in Judaism, but the violation of any of the 613 commandments would be considered bad. The word 'cheit' is what is most commonly translated as 'sin'. Cheit is...
No, however there is a Jewish law that states interest cannot be charged to a fellow Jew. Jews may charge interest to non-Jews, and non-Jews have no restrictions regarding interest (under Jewish law).