What is associated with: a female figure reminiscent of the statue of liberty has been this film companys corporate insignia since 1936?

Based on the clue 'a fellow traveler sympathizes with this party', what is the answer? What is associated with: a female bullfrog may lay 10000 eggs that hatch into these which may take 2 years to grow into… Based on the clue 'a female donkey or an early spinning machine', what is the answer? What is referred to by 'a female donkey'? What is associated with: a female horse age 4 or under rags to riches became the first in 102 years to win the belmont… Based on the clue 'a female horse of course', what is the answer? Based on the clue 'a female horse under the age of 4 or a lively lass', what is the answer? What is referred to by 'a female horse'?