What exactly does fold singularity do? The way I read it is, the building at the top of the build queue provides its benifits before it's construction is finished. Is that correct? What about ships? Is there any effect? The description about Fold Singularity doesn't say anything about ships so I'm surious.

Yeah, that's correct. The FIDSI or Approval bonus, as well as the upkeep cost, of the improvement currently being contructed is applied to the system while it is under construction. Construction still continues as normal, but may be sped up if that improvement provides a bonus to industry. Anything that doesn't provide a FIDSI or Approval bonus, such as ships, would be uneffected.

I can see this being potentially useful for new colonies with very low industry, where a single improvement could make a noticable difference, or for when you need that approval boost ASAP.  However, the +25% bonus from Compression Singularity or using Dust to buyout the construction is probably more effective in most situations.

Maybe I'm using Fold/Rip Singularity wrong, but it sorta feels like that tech can just be skipped.