Are rebirth, old age etc. 'dukkha'? Or, merely *characterised* by dukkha?

There’s 3 types of Dukkhas. As Buddhas are arahants too, the post I made makes it clear of which types of dukkha is still experienced by arahants, and which is not. In general physical suffering still exist because the body is still here, mental suffering doesn’t.

Dukkha in the broadest term refers to all suffering, mental and physical. Nibbana with remainders (arahants who are still alive) only have no more mental suffering, they still suffer physically.

In terms of Nibbana is the highest happiness, in that sense sukha should be understood with regards to nibbana. Sukha does have a more technical terminology tied with cessation of sukha at attainment of 4th Jhana, that’s not the sukha which is referred to when discussing about Nibbana as the highest happiness. So many words has many meanings. One has to look at the context to see the right meaning which makes sense.