You will be fine to leave them at the older version and then upgrade them slowly from there. There is no rush.
It is not critical to the guest, but the tools provide drivers and helps performance. Having "OK" tools means the guest OS has the latest drivers. I would say get to the most current version as soon as possible, but there is no need to create an emergency downtime just to update the tools.
You should be fine
As written it's not mandatory, but recommended.
For 4.0 to 4.1 I do not remember particular issues, so schedule this task when you can.
Usually not critical - and no major bug fixes between these versions.
What I normally do is package and deploy VMTools with my normal OS patches (so when I roll the Microsoft patch tueaday patches, I deploy VMTools in the same hit)