Simple brake test, pulling the brakes and pushing the bike by hand After installing and adjusting, there is this test, where you pull the front brake and try to push the bike forward, it should offer enough resistance to lift the rear wheel.

Then you test the rear brake, by pulling the lever and pushing... backwards? If I push backwards, it does offer enough resistance to lift the front wheel, but if I push forward, the bike will easily slide on the floor.

Is this correct? This seriously confuses me.

Test riding during rain or dry weather, the rear brake leaves a lot to be desired, it slows down, but seems like it takes ages to stop the bike. This isn't a question about braking technique, it's more about braking adjusting.

Is there any adjusting needed to be made in order for the rear brake to contribute for more stopping power, to make it behave like the front brake?
There are two tests for each brake. With the bike stationary, squeeze the levers hard to make sue that nothing is on the verge of breaking or has been mis-assembled. That test may seem silly but it reliably detects cables that are frayed to the point where they're dangerous, and also cheap shitty brakes (which will fail when you do this).

You can't effectively test braking power without having someone on the bike.  The force required far exceeds most people's arm strength (could you catch someone thrown at you at 30kph?). So, jump on the bike and grab one brake then the other, rocking backwards and forwards while you do so. That tells you whether the brakes work at all. If they do, start riding, then tap the brakes as soon as you're moving enough to do that without falling off. Make sure you're riding somewhere that a: you can fall off safely and b: you can stop safely without using the brakes. The whole point of these tests is that they might fail. If you're confident the brakes work reasonably well, find a quiet street or carpark and do more of those tests, speeding up slightly each time.

A good bike shop will have someone other than the mechanic that worked on the bike do this test (and a bunch of other tests) after they service every bike. Once you've done it a few times it becomes fast and almost second nature. Swing a leg over the bike while holding the brakes firmly, rock it a little, tap the brake as soon as you're rolling. That helps avoid nasty surprises.

If you have a front disk brake and not a through axle, that first tap will also tell you whether the front wheel is seated firmly in the fork. It will do that by lifting out of the fork, so it pays to keep that in mind (yes, disk brake mounts were designed for through axles on motorbikes, then the design was copied straight to bicycles with no thought whatsoever. My  bikes normally have the calliper on the right hand form blade, in front of the fork, so this can't happen)

Adjusting the brake depends on what sort of brake it is. Do a little research to find that out, then use the search box on the top right to find instructions for your brake (most likely it will be a V brake, but disk, calliper and cantilever brakes are all common too). Poor performance in the wet is normally a consequence of cheap brake pads, poor adjustment, or poor brake design (in that order, but you can suffer from all of those at once)