A. By what ages where men/women allowed to voluntarily join the Finnish army (upper and lower bounds if there was any, differences between men and women)?
I have scoured my few Finnish sources and can't find a definitive answer to what ages men were allowed to join the Finnish army. I will note that Mannerheim, born in 1867, was 72 in 1939 when the Winter War broke out.
Men aged 17 to 40 could join the Suojeluskunta ("Civic Guard") which was a sort of volunteer reservist training organization, but was not part of the military. Because the military budget was so small Finland could not afford to maintain a professional cadre of well-trained men to form the core of a wartime army. The men of the Suojeluskunta units (but not the units themselves) served to form this well-trained core.
Women were not allowed in the Finnish Army. Instead they could join the Lotta Svärd, a Women's Auxiliary which did jobs to free men to fight at the front. Generally they worked at hospitals, air raid warning stations, supply, and other auxiliary tasks. An explicitly unarmed and nonviolent organization, one group was formed into the 14th Searchlight Battery, placed under military command, and armed, though it never saw combat.
At first it was only Christian women who could join, but during the Winter War this was often ignored and by 1941 foreign, Muslim and Jewish women were allowed. By 1944 the Lotta Svärd included 242,000 women.
291 Lottas died, about half from disease, the rest in air raids and accidents.
Only in 1995 were women allowed to volunteer in the Finnish Army and be officers.
B. By what ages was service mandatory?
Never for women.
I could not find a definitive answer for men, but most sources suggest age 21. The strongest evidence is in "Manhood and the Making of the Military: Conscription, Military Service and Masculinity in Finland 1917-39" which makes several references to 21 year old conscripts.
...most young Finnish men in the 1920s and 1930s had a limited experience of modern disciplinary institutions when they arrived to do their military service at age 21.
What I did find is that the term of active service was 12 to 18 months, depending on the arm of service, after which they were moved to the reserve. Reservists over the age of 60 were moved to the militia. Source: World War II in Europe: An Encyclopedia