Hey, brave of you to jump in with K-3II and manual lenses! That's a great camera and interesting lenses, but the learning curve is steep, as well! This is why most people new to DSLRs start with a more simple camera and lenses with more automation. So don't give up, its complicated, but it will give you good results after some practice
But I'm not sure I completely understand what the question is.
In live view, you can change the display mode. In one mode, it only shows the picture, but in others you have more information, overlays, even histogram (but the histogram is not super helpful, I find).
The light meter on most modern cameras is not absolute, but it just shows you 0 (which is what the camera thinks should be a good, balanced brightness) and then +/- 3 or 5 and how far from 0 the selected settings are. So you can select if you want to under expose or over expose. With manual lenses, you have M mode with static iso number, where you press the green button and the camera will stop down to the aperture you selected on the lens, and then meter and select the shutter speed that fits the aperture and ISO. In Av mode, metering is continuous and you can choose Auto ISO range, but it will never stop down. Photos will be taken with wide open aperture. All modes except for M will default to Av, if you have a manual lens.
Now, Live view does
not always show the exact exposure you will get. This holds especially when you have fully manual lenses, long exposures, and so on. Some photographers complained about this since live view was added. Its not perfectly consistent, so you have to learn how it works. For example, if you are planning on under exposing a lot, then the camera will not show you that. Then you take the photo, and you will see it. Digital preview might help with this, but I don't usually use it. I just accept this, because with an OVF you don't always see the brightness that you will get, either.
For Bonus 4), maybe the lens has a little problem, where the aperture blades don't work normally. This can cause odd exposures. The other possibility is that the metering is different from what you expect, but still correct, just because the metering mode is set to spot meter, for example. I think matrix metering cannot be used with manual lenses. Or maybe you have EV +/- selected, or exposure bracketing. Double check all the settings that could affect exposure. And third, there is a possibility that the metering with the manual lenses is wrong. This is not super uncommon. What you can do to help with this is use a good, tight lens hood to block out unnecessary and stray light. But sometimes, the only choice you have is to learn a lens' character, and then adjust to it with EV +/-.
One more thing on metering in general.. sometimes we forget that we don't actually
need to meter before taking photos. These days, with manual lenses, I only meter when the light situation changes, like if I go from one scene to another, from shade to sun. I don't meter for every photo, I just meter to get the general idea, and then adjust by hand. With some practice, you can get a pretty good feeling for this. You can start by using the so-called Sunny 16 rule.
But please tell which lenses you have. There are different types of manual lenses, and they behave a little differently. Some are fully manual, like Mitakon or m42 lenses (best to just use Av mode, you focus wide open, and stop down the aperture by hand for the photo). Others have some automation, like Pentax M series lenses, but they still require stop down metering, because the camera doesn't actually
know what the selected aperture is - but it can move the aperture to your selection. Next is lenses with A setting (for example A series, Samyang lenses, and others) - where the camera can do pretty much everything except AF. If your lens has A on aperture ring, push the little button on the aperture ring and lock the ring into A mode, then leave it there. This lets you use P mode or Av or whatever. The next is full automatic, like F or FA or DFA or DA lenses, where the lens has AF and everything is done through the camera.