I am not a plumber, but I think I know what is happening. The "cap" is a vent to prevent a vacuum forming in the sink drain. It is spring-loaded and, without water flowing in the drain, does not allow air into the drain nor allow foul gasses out. My guess is the short horizontal run of pipe from the "T" to the vent is clogged. When the shower is running, the drain water forms a vacuum in the waste drain system. This vacuum pulls water out of the sink trap allowing the foul gasses to escape through the trap and sink drain. An unclogged vent would have opened and "killed" the vacuum. I believe your sink drain is improperly plumbed as far as venting. I suspect you have the infamous "S" trap rather than the desirable "P" trap and also have a problem with the bath drain venting

I'm not sure exactly why or how you think your have a leak? Can you post a picture...perhaps that would help. Typically if a pool is going to leak "inside" of the pool, it will leak around the light, around the pipes and drains or around the skimmer. I don't see how/why not filling the pool is going to make much difference. They can detect and fix that leak better when the pool is filled. Keeping it unfilled could create more problems and potentially a self-fullfilling prophecy.

I have to admit, I have started adding a wee bit of potting mix to some of my gritty mixes lately. Just to keep them moist longer. but I maintain that some of my succulents that just don't need much water really, really love the gritty mix. But I like watering the gritty mix, so it's no problem to me for smaller plants that can be carried back and forth to the sink easily. I think they like the frequent waterings. also, they don't need much watering once established. The most valuable thing I've learned from this forum is that different plants like different mixes. I mean, they can survive in one standard mix, but they can take off with customized mixes. I don't think I could use gritty mix for all of my plants like some do, but I do think some really thrive in it. if I grew outdoors, I wonder if I would feel differently.... just chatting. ETA: there are plants here in the desert that grow with no soil. The local cactus and succulent shops also tell you which plants do not need organic matter. The ecosystem here is truly unique and is largely soil -free.

A hospital where I worked had a stainless cleaner that smelled like WD-40 so I tied WD-40 and it worked. Most would dislike the smell I'm sure.