Absolutely no problem changing up the carpet. Things to watch for......make the transition in a doorway, an opening or along a visual break in the rooms (like the corners of the walls). I would stay in the same colour range, but just go to the other end of the spectrum rather than change the colour completely.....like light grey going to dark grey, not light grey going to navy blue. You want the separation but an easy transition on the eyes.

If you are seeking a truly open feel to the floor plan you have shared, then using one material in the mail living area is the best approach to making this space feel truly open. Using a variety of materials on flooring chops up the space and decreases the visual footprint. I would suggest using wood, tile, or if you are on a tight budget laminated flooring for the living/dining/kitchen. Then use carpet in the more intimate spaces; bedrooms and possibly hallway. Save the tile for the bathrooms.

There's no "method" to avoid it - you just have to avoid cut pile carpet as they'll all do it to some extent.

I think the brands you have listed are good! What colour were you thinking? How have you gotten the opportunity to import carpet? I hope it's not too expensive for you!