Are you trying to work out the signal polarity of each pickup by using a multimeter for resistance reading and then seeing whether the value increases or decreases slightly if you bring something metal up close to the pickup?

It really doesn't matter if the pickup values all go up or all go down, as long as they go the same way. If two go up and one goes down, then that single pickup will produce a signal that is the opposite polarity to the other two, and when used in combination with another pickup, you'll get a very thin wiry sound.

The Fleor pickup appears to be wired in the Seymour Duncan convention. Again, the the output signal polarity only matters when you are using it in combination with another pickup. A pickup manufacturer will normally be consistent in how they wire up and arrange the magnets in their pickups so that they all have the same relative polarity, but between different manufacturers, you'll find that some use one polarity and some the other. That's when it's important to check the polarity of the pickups.

If you have single coil with two separate output wires, then you can simply swap the connections over to change the polarity of the output signal if necessary. With a humbucker, if you have a 4-wire connection, then again you can swap over the hot and ground wires to reverse the signal polarity, but you will have to disconnect the screen from the original ground wire and connect it to the original hot wire.

What is a problem is if you have pickups, either single coils or humbuckers, with single wire + screen connections and the pickups have different polarities. You can't simply swap the connections over and use the screen as the hot connection, as the screen will then carry the hot signal and pick up a lot of electrical noise as it's no longer screened. You've then either got to partly disassemble a pickup so that you can do some very fiddly rewiring to swap the hot connection and screen connection over, or change the pickups so you have a set with the same polarity. You can opt to just live with the very thin nasal sound of mixed polarity pickups when using two (or more) together, and it can be a useful sound occasionally, but I do find that I prefer the standard sound a lot more.

Things become even more complicated when looking at Telecaster pickups (or related styles), as the Telecaster bridge pickup has a grounded copper plate underneath it, which will be connected to the bridge plate through the mounting springs. So even if you have a Tele bridge pickup with two separate output wires, you can't simply swap them over, as the hot output will be grounded through the mounting springs to the bridge plate and you get silence. So you then have to swap the bridge plate ground connection over. The Tele neck pickup also has issues here, as the metal cover is connected to the normal ground wire, so again, even if the pickup has two separate output wires, you'll need to swap that cover's ground link over (or disconnect it entirely as some people do).

And as Jim says, yes, the screening all needs to be connected to ground. This is normally done via the pots which will be grounded. they then touch the shielding on the underside of the control plate itself (or the metal control plate on guitars like a Tele), so grounding those items. You run the shielding tape up over the edge of the control and pickup cavities so that they touch the tape on the pickguard or the metal control plate so they become grounded. If you can. run the tape up to or close to one or more screw locations so there is positive pressure holding the bits of tape together. Pickguards can sometimes lift in the middle, so connectivity isn't always guaranteed unless the connection points are by the screws.

The shielding should form a complete as possible enclosure around the pickups and control components. Any gaps should be as small as possible.

Any separate cavities with shielding will need a ground wire run between them and back to a ground connection which can be another shielded cavity that is definitely grounded. I normally just use a piece of wire and tape down the bare ends with more copper tape.

You don't need to shield the trem cavity itself.