Short answers, pulled from the story.
The Theatre was built in 1576 by actor-manager James Burbage in partnership with his brother-in-law John Brayne. It stood in Shoreditch, just north of the City of London, on land that had been the grounds of the dissolved Halliwell Priory.
The Mayor and Corporation of London banned plays in 1572 and formally expelled all players from the city in 1575. Builders responded by constructing playhouses in the liberties just outside the city's jurisdiction, where civic authorities had no power to stop them.
Yes. Shakespeare was a member of the Lord Chamberlain's Men, which performed at The Theatre from 1594 until 1597. Some of his earliest plays had their premiere there, and at Christmas 1594 he was summoned with Richard Burbage and William Kempe to perform before Queen Elizabeth at Greenwich Palace.
The Theatre is said to have cost £700 to construct, described as a considerable sum for the period. John Brayne advanced the funds to James Burbage, receiving a share of profits and ownership of part of the property in return.
On the night of the 28th of December 1598, the Burbage brothers dismantled The Theatre with the help of carpenter Peter Street and ten or twelve workmen. The materials were stored near Bridewell and then ferried across the Thames the following spring to construct The Globe on Bankside.
In August 2008, archaeologists from the Museum of London excavating in New Inn Broadway, Shoreditch, found the foundation of a polygonal structure believed to be the north-eastern corner of The Theatre. The remains are listed as a scheduled monument and commemorated by two plaques at 86-90 Curtain Road.