Can Aniimo abilities be used to solve puzzles?

In practice this means you do not carry a separate puzzle toolkit. Your team is the toolkit. When you transform, the creature's abilities become yours to point at the world, and certain forms and abilities interact directly with world objects rather than only with enemies. Working out a puzzle is usually a question of which Aniimo you have on you.

The same transformation does more than unlock puzzles. It gets you past exploration obstacles and into areas you otherwise cannot reach, so the mechanic covers traversal and puzzle-solving with one button. It also hands you the creature's powers and combat abilities, which means the form you take to open a path is the same form you fight in once you are through it.

That overlap is the thing to plan around. A team assembled purely for combat can leave you standing in front of something you cannot interact with, and a team assembled purely for exploration leaves you fighting in a form you did not pick for it.

Water abilities and gated overworld areas

The clearest example is water. Aniimo with water field abilities can be used on environmental water puzzles, and those same abilities are required to reach specific overworld areas. That is a hard requirement rather than a shortcut. Without a form that carries the ability, the area stays shut and the puzzle stays unsolved until you come back with the right creature.

So some content is gated behind what you have caught, not behind your level or your gear. Catching broadly is worth doing for reasons that have nothing to do with combat.

Not settled: The transformation goes by three names in the closed beta build, merging, morphing and twining, all describing the same thing. Which one the game settles on is not fixed yet.