Why was there a need to rebuild the Globe Theatre?
The first Globe theatre burned down during a performance of Henry VIII
After the Globe Theatre burned down on June 29, 1613, it was immediately rebuilt with a slightly different design and ready for action the next year, 1614. After the second Globe was torn down in 1644, it was not rebuilt (since plays had at that time been outlawed), but a replica of the first Globe was built and opened in 1997. It is in a slightly different spot from the original.
You need to specify which Globe Theatre you are talking about. The first Globe (1599-1613) was home to The Lord Chamberlain's Men, renamed in 1603 as The King's Men. The second Globe (1613-1644) was also home to the King's Men. Shakespeare's Globe (1997-) has its own company. So does the Silvano Toti Globe Theatre in Rome (2003-)
No, the Rose theatre and the Globe theatre are two different theatres. The Rose theatre opened before the Globe theatre in 1587, and the Globe theatre opened afterwards in 1599. The Rose theatre closed in 1605, whereas the Globe Theatre was burnt down in 1613, rebuilt in 1614 and then closed in 1642. Both theatres are now rebuilt and open to the public.
The Globe Theatre was built in 1599. The theatre called Shakespeare's Globe was opened in 1997. The one Shakespeare acted in should never be called Shakespeare's Globe or William Shakespeare's Globe since he didn't own it and had nothing to do with its construction. For the sake of clarity, that theatre should be called The Globe Playhouse or The First Globe.