As far as the roof is concerned, yes, it is walkable, but not for everyone, so, just like with guns, motorcycles, chainsaws, or countless other things that can bite, YOU have to make an individual decision regarding your comfort level with it. It's not one that I would advise someone who has not been on a roof to practice walking on. And remember that there is a big difference between "look mom, I'm up here" and actually working on it.
As for your chimney though, they last a long time, so the plan should be to correct the problem before it needs to be completely replaced. The first thing that I would inspect is the crown, which is the concrete on top of the bricks. It should be concrete, not mortar, about two inches thick, overhang the bricks by at least and inch or so, pitched away from the flue, and no cracks. After that, check the mortar joints, as well as the bricks for any sign of deterioration.
Nice home by the way; I like it.