Plumbing – Why might our washing machine cause our clothes to smell damp when dry

Experience tells me that at least some models of washer won't hold water unless the drain hose extends above the water level of the wash basin. I can't quite figure out what you're trying to say about extending pipes, but it should be safe to have the water drain out of the washer drain hose at its maximum height.

Eventually, the drain hose can be high enough that the water column overwhelms the pump (or hoses), but you'd have to be doing something bordering on insane to reach that. Every foot of height in a water column adds .43 psi of water pressure, so even a hose rising 15 feet above the washing machine will provide less than 7 psi of back pressure. I can't imagine a washing machine pump which doesn't handle that.

Your problem is the sewer, not the "fresh" water.

Activity on another floor is almost certainly sucking water out of the sewer trap at your laundry and/or bathroom sink. The dry trap then has no resistance to rising sewer gas. Doing laundry fills the trap back up. Here's what it might look like in the wall behind your laundry machine. For proper operation the U shaped part must be full of water at all times:

We're talking China, so shoddy design or construction are a possibility. If the sewer trap is not vented, or is S shaped rather than P shaped ,it is vulnerable to siphoning dry. See https://en.wikipedia.org/wiki/Trap_(plumbing)

Test this next time you have the smell. Slowly pour about 1 liter of fresh clean water down into the drains near the laundry, and see if the smell starts to dissipate.

You can fix this by crudely mounting a second waste trap between the washer and the building's trap. This could even include an "automatic air admittance valve" just to act as a vent without the need to penetrate the roof or reach a window.