You already have a lot of answers to this, but I'll just add one more bit of information. The First Quarto states that Romeo and Juliet had been

plaid publiquely, by the right Honourable the L. of Hunsdon his servants.

This puts the composition date for Romeo and Juliet at or before 1596, even as early as 1591, because of a reference to the 1580 earthquake (Act 1, Scene iii, Line 22). This is documented by Neilson in Shakespeare's Romeo and Juliet on page 36.

After these early performances by the Hunsdon troupe, which changed its name after the 1590s, the first documented performance is 1662 in connection with William Davenant. Davenant, incidentally, claimed to be the illegitimate son of William Shakespeare.

In summary, the first performance, as indicated by the First Quarto, was between 1591 and 1596 due to the date of an earthquake referenced and the date at which the Hunsdon troupe changed its name. As to the number of performances, the Quarto only states that Romeo and Juliet:

hath been often (with great applause) plaid publiquely

The Quarto doesn't give a location for any of the performances, therefore it can't be said how large the venue was. You can read a little more about the performance history of Romeo and Juliet at Shakespeare-Online.com.

Historians have had trouble pinning down the publication date of this play. Some believe that Shakespeare wrote it around the same time he wrote his Richard II and A Midsummer Night's Dream, which means that Romeo and Juliet might have been written around 1595. By 1597, it had been officially printed. The first recorded performance of the play occurred in 1662, although historians believe it was performed earlier. However, by 1662, tragedies were no longer popular, so Sir James Howard's version of this play was changed to provide the audience with a happy ending.

As far as I know or can find, there is not good information about this. Romeo and Juliet was written before the inauguration of the great Globe Theatre, so it may not have been performed there. However, if it was, there is a lot of information out there about the Globe Theatre, so you may start with that and use it as a basis for the type of people in the audience and what kind of staging it might of had.