Thank you, Scott N!!! The culprit of my problem was the dislodged housing. Threaded or set screw? I was racking my brain because I could not find the screw using my phone in selfie mode to get a good view. With no screw in sight, I assumed my spout was threaded, so I gave it a twist, but I could rotate it only about an 1/8 turn. Luckily I didn't force it further. It was firm past the 1/8 rotation, and I didn't want to risk snapping the copper pipe, so I figured cutting off the housing was a safe experiment since I planned on replacing the spout anyhow. I cut around the circumference of the housing about 3 inches from the wall using a hack saw, being careful not to cut too deeply as not to touch the copper pipe inside. Once that was done, I used some metal snips to cut the housing (the portion closest to the wall) before peeling it off with some pliers. And low and behold, I found the set screw. As you can see in my second image, the screw was far misaligned from the space under the spout. Removal of the remaining parts was simple since I was then able to use an allen wrench to loosen the screw.

Did we have this discussion a few weeks back? Can you get another spout with threads that aren't recessed? If not, in my opinion it is much easier to do the job from the rear. You can leave some kind of acess panel which could come in handy. I tried messing with tiles once and it turns into a problem trying to mount replacement tiles on a backing that isn't secure. Also, there is a thicker teflon tape available. Could you try that with thread paste on top to see if that stops the leak?

As you've been told, with the pull-up diverter, you can expect some small amount of water to still come out of the tub spout. That is because the mating surfaces of the diverter valve are not always machined to be 100% water-tight, just sufficiently to provide enough resistance to water flow that the water will go up to the shower head. Some are more water-tight than others. You might want to look for a better one. The mechanism is all in the spout. A water-saving shower head may give enough back pressure so that more water may leak through the diverter than if you had a full flow shower head. The knob-type diverter valve will shut off the tub spout completely.

Not a silly question. When you have water forcefully hitting the inclined side of the tub high enough up, though most of it will splash downwards, some of it goes sideways, and some of it -- counterintuitively -- splashes back upwards from where it strikes the side and you can actually have a small puddle start to form on the floor in this area from water spray bouncing up and escaping this way. It the water doesn't hit the side of the tub, but only the bottom of the tub, it doesn't bounce high enough to do this.