Yes, the Baptistry is the dome outside of the Church. (One couldn't enter the Church without being baptized, so the Baptistry was a separate structure.)

I don't know, maybe 100 steps? Easy enough if you can walk a few miles without getting winded.

Thanks, 100 steps sounds good! do you get a good view?

There are a few windows/openings, but it's not the greatest view. Cool view on the inside however, looking down into the Baptistry.

PS The web site for making reservations to climb the leaning tower is www.opapisa.it/index.php?id=16&L=1&T=2

My husband and I climbed the tower 2 years ago, just after it was reopened. We paid for and reserved our tickets ahead of time. It was like a funhouse made out of marble! Not a difficult climb, but the level of the steps did change and sometimes you had to hold the walls. Still, really worth the climb, really brings the tower to life instead of just looking at it and taking pictures.

Brandie, Welcome to the 'I almost climbed to the very top of the Tower' club :).

I snipped this from my Pisa daytrip directions I posted here. Regards, Walter

When you get to the bell landing (1 level from the top) you will walk halfway around the Tower on the outside and then climb to the top.
There is a steel rail around the edge but there are 4 narrow steps that go longways around the Tower.
So your choice is to either walk right alongside the rail or on 1 of the higher steps which puts the rail lower in respect to you.
  I made it about 2 meters and got a major attack of vertigo (just like in the Hitchcock film:) and couldn't make it around.
But the other 29 people had no problem and in time my fingernail marks where I crawled back to the doorway will fade:).