This is thinking from the 1950s. All of these things have failed dramatically.
Anyway, if it was to me, then
a) I'm a cyclist (over 6000km and 115,000 vertical meters this year. That's further than I drove).
b) Of course pedestrians deserve space. I'd prefer to change the laws to allow non-helmeted riding on separated bike paths only, but that would be useless as where I live most separated bike paths don't link up which means people must either ride on the road or (illegally) on the footpath to get between them. In a world where not everywhere is Copenhagen or Amsterdam I'd prefer to see children ride to school with their parents on footpaths than not ride. I'd prefer to see people who worry about helmet hair ride to work on footpaths and separated bike paths than not ride. Where I live both these things are currently illegal.
c) Yes. Riding on roads needs to be made safe. That does not preclude encouraging more diverse transport choices by making other changes too.
I find too many cycling advocates come from entrenched pro or anti-helmet positions and aren't prepared to look for compromises. That isn't helpful overall.
However, I used to be strongly in favour of mandatory helmet laws. Now I tend to think they need to be more targeted and used as a blend of changes. I think riding on footpaths should be allowed (with a strict speed limit) without helmets, as well as on separated bikepaths, again with a speed limit. On roads they should be mandatory.
[1] http://i.imgur.com/qPGUfAK.png