You can always use a skill you're untrained in, and you can use it in any way not marked as (Trained Only). Being trained means higher numbers, and unlocking the trained only applications of the skill.
Consider Athletics and Acrobatics: nobody needs training to be able to jump, climb, swim or balance. (At least, adventurers are assumed to be minimally competent at this stuff.) However, Acrobatics can also be used to Reduce Falling Damage (Trained Only) — only people with special training in Acrobatics can do this.
In your specific circumstances:
Using Arcana for monster or arcana knowledge isn't trained only. The fighter can do this. It isn't unreasonable that someone would pick up a thing or two about magical stuff if they're living and adventuring in a world full of magic. To them this is just being reasonably educated about the world they live in.
- The fighter wouldn't be able to use Arcana to Detect Magic, though, as that's trained only.
Unless they're trained somehow, of course.
Same goes for the Wizard making a Dungeoneering knowledge attempt. They can do this. They've probably picked up a thing or two, heard songs, read stories, been told fables about the Bulette (some of them actually reasonably factually accurate!), or so on.
Using Thievery to Open Lock isn't trained only. Everyone can attempt it.
In all of these cases, being untrained doesn't mean you can't do it at all. But being trained helps, because it means you're going to be better at it than anyone who isn't. If you're trained in a knowledge skill, you'll be more likely to have Expert or Master knowledge more of the time. If you're trained in Thievery, you'll pick the lock sooner than untrained people who will fail a few times before breaking the same lock, and be able to pick Paragon or Epic locks they wouldn't have a hope of opening.
