Of course, can be a lovely combination.

Yes - but choose your clematis variety with care,according to which type of rose you've got and how large it gets. Roses like good airflow round their stems and foliage, so choose a smaller clematis variety from the viticella or jackmanii group (prune group 3) because those are cut almost to the ground in winter, meaning the rose isn't permanently covered with clematis growth all year.

Must be nasty and painful business to remove dead and overgrown clematis vines from a rose bush....sort of like untangling a fishing line strung with hooks I imagine.

Depends on the rose variety as much as anything, Loosestrife - over a rambler, yes, pain in the butt, but up a climbing rose, its okay, yoiu just cut it off at the bottom and tug. Harder to get the dead growth out of clematis mesh, to be honest, though of course, there's no thorns to contend with.

"Ground cover" roses, such as some of the lower Mediland varieties, ought to be ideal root shaders for Clematis varieties.