Yes it does and chimes the time every 15 minutes.
Yes, Big Ben is still called Big Ben.
Yes, Big Ben is still standing to this day.
No, Big Ben is still standing.
still in London
yes
Yes, you can still visit it in London.
yes
yes although it has its nicknames. In 2012 the tower which houses the Big Ben bell, is being named The Queen Elizabeth Tower in honour of Her Majesty's long reign.
not any more
during the London blitz big ben did suffer some damage, but continued to work throughout
Underground work on the buildings around it
Big Ben !