I believe those are the correct part numbers for the pipes. I did find a part number for the clamps near the waterpump pipe to be different than the one you listed (805922090). The prices for the pipes are quite obnoxious though.
I think LM22090 is good. It says it's not for use in limited slip differentials which means there are no friction modifiers.
If you're not set on Liqui Moly, use Motul gear 300 or Mobil Delvac. Both work well in subaru 5MTs.
I believe GL-5 oils are all hypoid gear oils. You just need a GL-5 within friction modifiers. This is due to the fact that the front differential of the 5MT is inside of the transmission (shares the fluid). The center diff is sealed so it doesn't matter. So we need a gear oil robust enough for the front diff and mild enough to not eat the synchros.
Did you add petroleum jelly or anything to prime the oil pump?
You can try this: Remove the oil filter and crank until oil comes out. Then add filter, replenish oil and start.
One other great option for oem parts is partsouq.com. Massively discounted and worldwide 2-3 day shipping.
Also, I think the NTK is the oem supplier for vvt actuators.
Found it. It's 05 sti and 7mm depth. I bumped the thread with the information. I'd love someone to try this as it would really make full brembo swaps easy.