You get a stronger version of a pet you already own by collecting more copies of the exact same pet and combining them in the Fuse Machine for one higher-rarity version.

Yes, Trails do more than look good, they also give a speed boost, which matters since Speed determines which biomes you can safely reach.

Not entirely, a pet's size and mutation roll can meaningfully change its actual income, so two pets of the same rarity can perform very differently depending on how they hatch.

Yes, you keep the Pets, Trails, and gamepasses included with my purchase, exactly as shown in the listing.