The chain needs to be long enough to engage bottom gear on the cassette, while on the biggest chainring(in theory!) with enough slack to make the change smooth. Any longer is too long

As always, there is plenty on the SB site and elswhere on the best way of doing it.
It's probably right - was installed by a bike shop for the guy I bought it off .... just didn't know if you could change / tweak the tension of a fixed length chain. Without looking into it, I'm guessing probably not !
Re open cables....Frame flex can cause screwed up gear changes, especially if the cable is routed via the downtube and BB. Alfines have been know to change gear on their own by frame flex while offroading.
Interesting. Cable routed via top tube on the MTB (but that's derailleur) and the bike with Alfine they are internally routed inside the downtube (it's a Step-through). The frame on that one is very heavy duty though and it isn't suitable for any real off-roading. I'd guess that if there is flex in the frame it would most likely happen with consequence for gears at the rear axle. Equally possible is that the wheel in those cases wasn't secured back in to the dropouts tightly enough ! This might lead to slight movement of the axle in the dropouts.
My own experience has been that with horizontal dropouts (and freewheel in chainwheel), insufficient torque on the nuts can cause slight wheel slippage which in turn leads to loss of chain tension. This has a huge effect on the hub gear tuning and always leads to slippage. I struggled for ages to work out the source of gear slip but having worked out how to get the wheel really well aligned and secured, and the chain tight, the gears have miraculously behaved themselves perfectly ever since (touch wood !). It's a finely tuned system but one which seems to work very well when set up as intended.
I've had gearshift problems with open cable while experimenting with a battery bag on the top tube. Total weight was under 3Kg, but changes up got clunky on several occasions. May well depend on the design of bag and the fabric.
This one would look a bit like this - albeit made for a hardtail triangle and not a full-sus :
Bike Bag Main Options Page
You can see the attachment flap at the top of the bag. This would be velcro sewn under 1000d Cordura to match the rest of the bag. In the context of the OP photo above this flap would be wrapping around the top tube over the exposed gear cables running along the tube between the moulded guides. The material is almost certainly too thick to go under them. My logic concludes that this will compress the exposed cables down to the frame and put pressure on them. Given that the cables move back and forth as gears are shifted up and down, this must surely result in their efficient operation being impeded (or at the very least some friction) unless the wires are enclosed within a more rigid sheath that they move inside. However, maybe I am incorrect in my preliminary logical analysis

It's hard to be sure without having something to actually try.
On weight, the total of bag + contents likely about 6-7kg. The weight of the bag contents will be taken mainly on the seat post tube / down tube (it will house battery and controller etc). But to get a strong and stable fit I'm pretty sure the top flap would need to be tightly closed and be subject to both downward and lateral tension. The bag width immediately under the top tube would be 3.5" min., so to wrap flaps of that width securely over the top of the tube would most likely compress a wire located there to the frame (but probably not compress a cable routing housing enough to interfere with a wire cable shifting inside it). Hence thinking I need to house the currently exposed wires ! Hard to explain but hope that makes sense !