1 - not irrelevant, it's a wider lane. Lane width counts. Especially if you've young kids, prams etc.
If we accommodate large vehicles, then the minimum lane width is 2.6m (2.6m being the maximum allowable width of a vehicle excluding mirrors). Assuming a 2m train (parent + buggy) that'll take about 7s to cross at 1.5mph (I walk at 4-4.5mph on the flat). If we increase the road width to 4.5m (3.65m is the width of a standard motorway lane) then the time taken to cross increases to 9.5s. In the grand scheme of things it's a negligible difference for crossing time.
However we look at this from a cyclist being squeezed point of view there's a huge difference. My big car is wide in the grand scheme of things, total wing to wing width being 2.03m wide (2.146m mirror to mirror), at 2.6m lane width as a cyclist I have a maximum of 0.5m to survive in if someone try to push through regardless. But the reality is the driver will be about 20-30cm from the kerb naturally so it's a real survival space problem. Now go to a 3.5m lane. With a 0.25m kerb clearance for the car & cyclist you've got about 0.7m space for the car to pass, that's not going to be safe in the slightest considering any slight wobble from either will likely result in a collision. At 4.5m I've got 0.6m to the kerb, the driver has the same & there's still 1.1m of survival space for me. Comfortable, no, but reasonably safe.
2 - on a existing road, if you increase the lane width, the island would have to get narrower, the roads a fixed width - it's not like they're going to reduce the width of the pavement?.
Depending on the situation why not? If the road won't support narrowing of a pavement or allow for a decent lane width a central refuge is probably the wrong answer anyway.