yes, women have been allowed to compete since 2000
Water polo, wrestling, weightlifting.
The number of competitors depends on how many countries send athletes for that particular Olympic sporting event. In weightlifting there is also many weight classes. In the Olympics there are 7 weight classes for the women and 8 for the men. Each has a varying number of competitors.
Yes both men and women take part
According to http://en.beijing2008.cn/news/sports/headlines/weightlifting/n214520710.shtml (BEIJING, August 9) -- Chen Xiexia of China performed with the confidence of a champion throughout the Women's 48 kilogram Weightlifting competition on August 9, successfully completing all her attempts for a gold medal finish with 95kg in the Snatch and 117kg in the Clean and Jerk for a total of 212kg, a new Olympic Record.
The silver medalist of the Women's 48 kg Weightlifting event at the Rio 2016 Olympics was Sri Wahyuni Agustiani.
Hiromi Miyake was the bronze medal winner in the Women's 48 kg Weightlifting event at the Rio 2016 Olympics.
The trampoline became an Olympic event in 2000. There is no first women in the trampoline event. The link below has who what won medals in what year.
None.
The Marathon
María Isabel Urrutia in women's weightlifting, heavyweight class, at the 2000 Games in Sydney.
The country that won the gold medal in the Women's 48 kg Weightlifting event at the 2016 Rio Olympics was Thailand.
Indonesia was the country that won the silver medal in the Women's 48 kg Weightlifting event at the Rio 2016 Olympics.