Final answer:
The famous theatre built by a syndicate headed by actor Richard Burbage in 1599 was called the Globe Theatre. It featured a thrust stage and an open courtyard where the audience stood. Women's roles were played by men during Shakespeare's time.
Step-by-step explanation:
The famous theatre built by a syndicate headed by actor Richard Burbage in 1599 was called the Globe Theatre, option a).
The Globe Theatre was a renowned Elizabethan theatre located in London. It had a round ground plan and featured a thrust stage, where the stage extended into the audience. The theatre had an open courtyard where the audience stood, and it housed Shakespeare's productions during his time.
Women were not allowed to act on stage during Shakespeare's time, so female roles were played by men who were trained from a young age.