1. Is it a good move to run totally fanless? Either I use the custom heatpipe cooler or I use the stock intel cooler.
If you go that route, don't use the stock cooler. Either fanless or a different enclosure.
BTW, is it a good move? I can't help.
2. If I use the custom heatpipe cooler, do I put artic silver on the heatpipes that attach to the sides of the case?
Thermal paste always helps: but use a different compound, AS is not that good nowadays.
3. Would it make sense to shoe-horn a decent 90mm slim fan in there and run it slow?
Seemingly that enclosure doesn't have proper ventilation holes, so a fan could mostly recirculate hot air: I don't think it will really improve the relevant thermals but just try it, in case.