That's fine. Although tbh, you can use 4000k for kitchen too - just make sure it's bright enough, above 800 lumens.

Yes square shape easy to be installed wrongly, often times "senget" because now a days the bangla workers can't cut a proper square into the plaster ceiling.
If it's round then obviously there's no way to be senget, logically speaking.

For places where there is a risk of accident, of course you'd want it to be bright. A bright area subconsciously heightens the human's senses, but don't be mistaken between brightness and temperature. Kitchen, store rooms, maybe even the shower (although the shower is a lot more subjective, some people like a very "relaxing" shower) - should have brightness of above 800 lumens.

For downlights, I usually just use Phillips. I've had it with all those no-name downlights - the part that spoils in them are the drivers, not the LEDs themselves. It's gets rather annoying to change eventhough it isn't difficult.

Yes.

You can choose higher wattage (though be wary, because wattage now a days is used as a marketing tool and no longer for actual measurement) or more downlights. Location of the down lights in the ceiling is also kind of important, don't just lump them all together or spread them out too wide.