- you are right, a delay of 8 does mean the factory is out of service for 8 days, so no production or research.
- your assumption, that you will get the Ta-152 H after 517 days is not correct, you will get this factory after a delay of 517 days. After this it will contribute to research or production.
General: How long do I have to research, to get a machine that is scheduled for the future
Rule of thumb: The first month cost 100, the second 200, ..., the 8th and all >8 cost you 800 each)
+1 month - 100 machines researched (single engine w/o special rules: 100 frames AND 100 engines, a BV155 does require 4 engines/frame so you need 400 engines)
+2 month - 100 machines researched + 200 machines researched = 300 machines researched in total
+8 month - 100 machines researched = 100+200+300+400+500+600+700+800 = 3.600 machines researched total
> 8 month: Add 3.600 + n*800
Each research does require frames and engines, so to get a FW 190 A8 you need 1 frame and 1 engine, for a Me262 you need 1 frame and 4 engines.