Stair Rods are entirely decorative nowadays, most fitters will fit a stair runner in exactly the same way wether rods are being used or not, they sipmly fit over the top (provided you order the right ones with the right brackets in the right size.
For underlay, ideally use a crumb rubber product like Duralay Treadmore, it is a low height but very hardwearing and is less visible in profile when seen from the side if you have open stringers.
How you fit the carpet on the turn etc will depend on a few things, the type and style of carpet and personal preference/skill level.
To be honest, a good quality stair runner and stair installation with stair rods on an installation on a turn like you have is best left to a profesional fitter, it's probably the most difficult carpet fitting job to do properly.
Essentially, a fitter will visit , measure, quote, he would then return to measure everything up and cut the carpet down to the various shapes and sizes, take the carpet away and have the carpet edges whipped or finished to spec, then re-visit to fit the carpet, lastly it's often the case that the fitter will then measure for rods, order and come back and fit them if they are solid rods made to order. If you go for cheap hollow rods, these can be pre-ordered and cut to size on site but are not as hard wearing and won't look as good.
We use
http://www.stairrods.co.uk/ for most of our stair runner accessories etc.