The common sense way, followed by most radio hams, is not always strictly according to the rules. In my town for example, permits and inspections are required for any wiring beyond changing a lightbulb, including low voltage like loudspeakers or coax. This is my common-sense take, you could also ask a licensed electrician.
1: Gas pipe etc: If the chimney is hot metal, not cold plastic, then you should worry about it somehow igniting the coax. Coax might burn, and in a well hidden vertical shaft deep in the house that's not good. At minimum, find a way to secure the coax away from the hot chimney. Also test the chimney temperature with your hand. My ancient furnace exhaust gas is about 200 C / 400 F and the pipe runs against some wooden framing with a little half-inch metal spacer thing.
Is the shaft wood or brick? Is there already something non-metal in there, or just a metal gas pipe and a metal chimney? If it's not a general-purpose cable-and-pipe duct, you may be breaking some rule by adding a flammable cable to it.
FEP/PTFE cables are good for up to 200 C and can't be ignited. RG400 would be fine for HF.
I wouldn't worry at all about the gas pipe being near the coax. It will be a heavy metal pipe, tested for air-tightness. Gas pipes run all over the house near to regular electrical cables carrying 120 V and many amps. Just don't damage it mechanically.
2: You always need to worry about lightning.
Keeping the antenna indoors will make it more according to code, so if something bad happens they won't be able to blame it on your antenna, fairly or unfairly. Any cable that runs from outside to inside needs to be protected in specific ways - at least grounding the shield to an earth rod, like a cable TV coax is. This is also good practice, will reduce the chance of huge sparks flying across your shack.
Apart from that I don't see much difference between the antenna hanging just under the plywood, to one draped on top. It's still the highest metal object in the house. Some suggestions for protecting your indoor-antenna setup:
- Ground the radio chassis to the mains earth with a separate solid wire
- Better, have the coax go through a barrel connector on an earth plate, and ground that.
- ground the plate to an outdoor earth rod
- pass the mains power for the shack through a surge protector mounted on the same earth plate
- use a coax surge arrestor suitable for your frequency and power level, install that through the ground plate instead of the barrel
- run a separate #0 / 10 mm^2 ground wire from the antenna directly to its own ground rod by the shortest path
3: A balun is a good idea - it will improve the antenna performance and reduce the RF on the coax. At QRP you can even get them from Amazon etc.
With 5 W you won't cause much trouble to your computers and TVs in the house, but by reciprocity if the coax is part of the antenna, it'll also conduct all sorts of noise up to the antenna. The balun will eliminate some of this common-mode noise.
For 100 W, you should think about what happens if the balun or antenna overheats and catches fire during a long digital QSO. It's unlikely, but it's also lying against the wood where you can't see it. Consider a balun in a metal box. Mount the antenna feedpoint away from flammable materials.
More than 100 W you start to have the risk of arcing too, it might be safer to take it outside.