Is it accessable for someone with slight mobility problems? Are there places to sit down?
It depends what you mean by "slight" mobility problems. If, as I assume, you are able to walk limited distance with some assistance, please bear in mind that the site in total is 8 acres in size so you might not feel like walking the grounds, ramparts or wartime tunnels as they cover some distance with limited opportunities to sit. You should avoid the Norman keep with its many steep steps. As for the main building and its lavish rooms, this is the advice given on the castle's own website regarding entering the main castle building. https://www.cardiffcastle.com/accessibility/