Can I include carrots in Tortilla de Patatas and can I use a casserole dish to make it taller?
If you would like to add carrots, make sure you cut them small enough (since it takes quite a while to get them soft). I'm not 100% sure it would be a good fit, but that's up to you.

You certainly can make a tortilla in the oven, I've done so in a spring form. I think I did it for about 45 min in an oven of 180°C/350°F. But this depends of course on how much food you use and how big your form is. Just keep an eye on it, the egg should be fully cooked and the potatoes soft.