Since 1936.
Archery was a sport at the 2016 summer Olympics. Artistic gymnastics has been a Summer Olympic event since the 1928 Olympics. Alpine skiing is a Winter Olympics sport.
No. Brazil has been represented at the Winter Olympics since 1992 by athletes participating in alpine skiing, bobsleigh, cross country skiing, luge, and snowboarding without winning any medals.
No. Through the 2010 Games in Vancouver, South Africa has been represented by athletes in alpine skiing, cross country skiing, figure skating, short track speed skating, and skeleton without winning a medal.
Karate is not an Olympic sport. However, Tai Kwon Do is an Olympic sport and there have been a number of gold medals for the United States in this sport.
It has been an Olympic sport since 1763 and is still being played today.
I think skiing started in Scandinavia as a mode of transport. Sandre Norheim of Norway is known as the father of modern skiing and was considered one of the best skiers at jumping, parallel, and Telemark style turning during the 1800's. From there, skiing was brought to the Alps and the US. Skiing might have been invented separately in China, but I'm not sure about that. Alpine skiing came around in the Alps in the 1880:s.
Pentathalon
No and has never been
Cross-country skiing has been used for centuries in colder climates to get from one location to another.
Karate has not been demonstrated as an Olympic sport yet.
Chess has never been played at an olympics. Nevertheless, it is an official sport recognised by the International Olympic Committee. This means that it could be added to the olympic program at any time if the committee wishes. Other examples of sports that are recognised while not being in the olympics are water skiing, karate, and bowling.
From 1928 - 1948 and from 2002 - present.