I only use alchemist when i lack space to shrink my lumber mills, i still don't have a good idea how to build my lumber mills and how u get the most profit, the repair factory's for example.
Do they increase lumber generation rate?
Do they increase lumber mill build time?
Does the benefit of the Repair Factory's stack ? example:
Do they increase lumber generation rate? not directly.
Do they increase build time? they build faster (increasing build time would be slower lol!)
Does the benefit of the repair factory stack? you mean the repair? yes. Two repair factories (or more, see my screenshot) can help build the same building (not necessarily a lumber mill)
So now we know this, we also need to remember the fact the alchemist can place them wherever, so not necessarily in the same place they were made, so the idea is, to make an efficent lumber production area, then to make the alchemists build them in a corner out of the way.
Example:

all of factories highlighted in green are close enough to help "AUTOMATICALLY". This is for 5.2, Niwa has apparently made it more reliable for repair areas in 5.3 when it's released. Sometimes it won't happen, especially when you build where your worker is, your worker will jump out the way and begin building but often this confuses the system and causes the factories to not automatically help and you need to select them manually (if you notice that is)
As some form of proof, this is where 6 factories are helping to make it, they will automatically do so with this setup in that middle space (5 help at the closed ends and 4 help at the open ends, i dunno i just like the look of this setup).
With 6, it produces a lumber mill in ~6 seconds, with 4 it produces a lumber mill in ~10 seconds.
screenshots:
check the replay timer and the "survive..." timer:
I'm pretty sure the build time without any factories is around 20-25 seconds. With a single factory, it's reduced by roughly 5 seconds. (a factory and 5 lumber mills is faster to build than 5 lumber mills alone, or something close to that)
hope that's pretty clear for you!