It's not random, the result will always be the same species from that combination of parents.
Species A + Species B = Species C
All combinations can be found here:
https://docs.google.com/spreadsheets/d/1YgPc11dgdBUC8jXNp01b7gI6jNHoBRQGwrY_V6lXMgQ/htmlview#gid=129871166
Column + Row = Result

All Passive Traits are inheritable. It's unreliable, but you do have a noticeably higher chance of them inheriting. You are able to get any 4 of what you want.
~~Lucky is the alternate translation for Rare across platforms. Lucky / Rare = Bigger Model. Big =/= Better (they can get stuck in your base).~~ Most of the alternate translations seem to have been ironed out in the last Gamepass update.
Legend seems to be one of the best traits (+20% to Attack / Defense / Movement).
There will eventually be more info on Traits and Skills.

IV's / Innate differences do seem to exist, but it's unknown how much so. Best to get your Attack and Work Speed this way via breeding, because putting points into them is a spook.

Bonus FAQ / QoL / Minimal Spoilers:
The top-left corner of the map (the World Tree) is currently inaccessable for later content, with a massive invisible wall. Careful if you're travelling over the sea there, so you have the stamina to cross back.
Catch 10 of each Pal for a large XP boost that scales with your level.
In the party menu you can click on Pal Powers and swap them with any the Pal has previously known for free while out of combat.
Captured Traders still cycle through their wares.
For movement, combat sliding down a slope gives a massive boost of vertical speed. Alternatively, jumping on a Capture Ball, then it successfully capturing a Pal, will blast you up in the air, getting you a ton of airtime. Combine with gliders to get where you want. Both are conditional / unreliable, but they're the fastest movement techs in the game known right now.
Grappling Hook helps you move around while overencumbered. Before then, stack Pals with increased Equip Loads.
You can build (almost) anywhere, but you can only access the materials from everywhere within your base.
Apparently there's a waterfall-cave you can build behind, if you want a cave-base. Somewhere. We don't know where.
Expect some jank.