Couple of questions I forgot to ask on grappling.

If you do a takedown or trapping maneuver, do you have to win the roll to trap or knock them down before you can do damage, or do you just have to hit with the attack?

And when it says you can do damage at half your base, does that include the strength bonus? Or is the strength bonus added after you halve the base?

And if someone has you trapped in a grapple, how do you escape from it?

Finally, if you're knocked down does it cost you a minor action or a standard action to get up?

Couple of questions I forgot to ask on grappling.

If you do a takedown or trapping maneuver, do you have to win the roll to trap or knock them down before you can do damage, or do you just have to hit with the attack?

No, you don't have to win the actual trapping/takedown roll. Having someone barrel into you or grab your arm and yank still hurts even if they fail to knock you down or immobilize you.

And when it says you can do damage at half your base, does that include the strength bonus? Or is the strength bonus added after you halve the base?

Base Damage is before strength. Base Damage for Grappling is 20, so half is 10.

And if someone has you trapped in a grapple, how do you escape from it?

You can make a characteristic check each time your initiative comes up. If you can't take active actions, then you go at the end of the combat turn. If you are fully immobilized, you can't escape until the attacker lets you go.

Finally, if you're knocked down does it cost you a minor action or a standard action to get up?

No such thing as a minor or standard action in Anima. The book doesn't say, but I would say it's a Passive Action with a penalty to your Active Actions taken.