What's the reason of kaparot? Why with a chicken? Why do we shecht it? And why on Erev Yom Kipur (can I do it every other time of the year)? Is it halacha or a minhag? Thanks
There is a comprehensive article which addresses each of your questions here:
The custom of performing kaparot with a chicken dates back to late Talmudic times. The earliest extant record specifically discussing the use of a chicken is a responsum from Rav Sheshna Gaon who lived in the early Geonic (post-Talmudic) period (approx. 660 C.E.). Rav Sheshna takes it for granted that his reader knows about the custom, a clear indication that it was widespread at the time. Some commentaries point to passages in the Talmud itself that allude to this custom.
Several reasons have been suggested for the choice of a chicken to perform the kaparot rite:
In Aramaic, a rooster is known as a gever. In Hebrew, a gever is a man. Thus we take a gever to atone for a gever.
A chicken is a commonly found fowl and relatively inexpensive.
It is not a species that was eligible to be offered as a sacrifice in the Holy Temple. This precludes the possibility that someone might erroneously conclude that the kaparot is an offering.
...We ask of G‑d that if we were destined to be the recipients of harsh decrees in the new year, may they be transferred to this chicken in the merit of this mitzvah of charity.
It is important to keep in mind that the chicken is not an offering. Neither does performance of the ceremony alone atone for one’s sins. However, the ceremony does shake one up a little.