What happens when one assigns a resource share of "0" to a project?

It depends on the version. Later versions of clients and projects are supposed to only work on that project if no other project supplies work. Older versions get divide by zero errors and crash. I would advise using 0.001 instead.

I ask for this reason: I need to set a project to NNW for all my machines. I do not want to detach, because I want to avoid creating multiple host IDs, when eventually reattaching. The only way to set NNW today in BAM, it individually select each machine I(same applies to gracefully detaching). With large farms, that is not practical.

So if I understand you correctly, the smallest unit I can use is ".001", correct for older projects. But projects created (say) within the last 4 months, will act as NNW if set to "0"?

Correct. But use "0.001" with the leading zero, inputs may be trimmed to the first number.

I used to set the resource share to 0 for my inactive projects, and via BAM! it has always worked (while setting manually sometimes resulted in a reset to 100).

But it seems as if the newest server software does not support it anymore... On SETI@home or PrimeGrid I can set it to 1.0E-101, but when I set it to 0 (via BAM! or manually) it is reset to 100.