I personally am quite happy to have sex during my partner's period, but it is very much a matter of choice for the lady concerned.
As far as anal sex is concerned, next time you are 'in the moment' - try tickling her bottom gently and see how she reacts. If she stiffens and stops, you know it's a no-go area, and if she seems to like it, carry on and explore, and then you can 'pillow talk' your way round to the possibility.
Asking over the dinner table is NOT a good idea - time and place and all that ...