This is not a technical question, but rather one of convention.
How should divided highways be mapped? I am not really happy with either of the two obvious options.
a) Show as a ‘normal’ primary or secondary road, however this does not show the restrictions on crossing the painted divider except at the designated crossing points.
b) While a dual carriage way gives the correct restrictions a divided highway does not ‘look’ like a dual carriageway, and has problems with turnoffs on the ‘wrong’ side of the road. This does raise a corollory question.
c) How are such dual carriageway turnoffs handled?
Which approach is ‘correct’. or is there another preferred option?
The general consensus is that you draw a line for each separate physical feature. So if your highway is physically divided you draw two separate lines, otherwise just one.
On the subject of turnoff handling: there is much to be improved in OSM. There are some propositions on how to handle them, but no consensus has been achieved. Currently there is a big discussion on how to handle e.g. turnoffs better (and many other advanced relationships), so I think it’s best to be patient and wait with implementing turn restrictions until a proper infrastructure is in place.
Looks like you’ve found the answer yourself already, but:
No, it’s not necessary to map a walkway directly besides a way (it is assumed that pedestrians can walk on certain types of roads). If a walkway is separated from the way by e.g. a patch of grass you can choose to draw that walkway as highway=footway.