Permanent Residency application - volunteering? length of stay?

I'm relocating to Singapore and am interested in applying for PR at some point in the future.

Volunteer work - What type of volunteer work do the SG authorities look favorably upon? Does it need to be a leadership position? A large number of volunteer hours? Are there specific types of volunteer organizations they like?

Length of employment - Do you know anyone who's gotten PR during their first 6 months working in Singapore? If I can get some really impressive job, would that be possible? Or does pretty much everyone have to work here at least a couple years before getting PR?

Getting a PR is extremely tight, unless you bring few millions into Singapore.

Secondly, you can apply after working here more than 6months but the application would be reviewed case by case on merits base.

Thirdly, volunteer work is always an advantage but not enough to decide the fate of your application. Singapore always wants what r you giving to society and what & how are you providing your valuable experience in Singapore

Basically, to become PR you need to show that you are adding value to Singapore as an economy and as a society.
The decision criteria are are unpublished and somewhat flexible.
As Surya said, a huge investor, famous scientist or world-class athlete could become PR quickly, for people like you and me a minimum of three years work, plus other factors (e.g. volunteering) is needed. Race also plays a role (Chinese ancestry preferred, Indians less so).
But it is very well possible to live and work in Singapore for many years on a work pass without applying for PR.