I think they are pretty durable, as long as they aren't dropped from I huge height or on the ground (like concrete) Even then, they are quite durable. As my 3 yr old often 'borrows' her big sisters tablet and has dropped it on ground a few times and it's fine.
Yeah, she loves it(even if it's not her's) and is actually much easier for her to navigate then the Leap Pad 2. As a friend's boy has one and she got quite frustrated with it.
Don't know much about profiles, maybe do some googling. But to avoid the internet surfing, either keep your wireless turned off at home, when your toddler is using the tablet or just make sure that wifi is not enabled. If your wifi is password protected there will be no issue though, as even if your toddler taps the wifi settings on tablet, they can't enable anything without your password.
Hope that helps
Edited by escadachic - 18 June 2013 at 4:47pm