Some powers make breakaways pointless like leap/climb. Can I put the Shake off feat on a character and make him or her breakaway to try for the one damage though?

SHAKE OFF
Prerequisites: Transporter or giant character
Choose a character.

When the character successfully breaks away, it deals 1 damage to all adjacent opposing characters.

Also is breakaway a move action? If so can I give DC75th Batman a free action to attempt a breakaway while adjacent to a red line?

ROOFTOP TO ROOFTOP: Batman can use Leap/Climb. Once per turn, if Batman has no action tokens, he can be given a move action as a free action if he ends his movement adjacent to a red boundary line.

If all this works together can I add armor piercing and do one penetrating damage for free?

Choose a character.

Damage dealt by the character may not be reduced below 1.

Well Breakaway has to be rolled when a character moves away from an opposing character. So moving from free actions would work. However; ignoring characters for movement means you don't make a breakaway. So I don't think Leap/climb is a may use power. If it can't be ignored then no breakaway.

He automatically breaks away. So you dont have to roll.

Automatically? So in other words with the shake off feat every use of leap climb can activate it?

Breaking away is not an action, it is something that happens when a character is moving due to being given an action. It does not matter what kind of action was given though.
If you want to break away you could always declare a vanilla move action. I am unsure if you can choose to break away when using Leap/Climb though.

No. Shake off only works when a character actually rolls for breakaway. No roll, no damage.

Break-away is not an action. Break-away is required when (a) you give the character an action to move and (b) they begin the movement adjacent to an opposing character.

Leap/Climb ignores characters for movement, and it doesn't allow you to not ignore them. But you have to activate L/C with an action.

So you can choose to move without using Leap/Climb, in which case you would not ignore figures and would need to roll for break-away. And if successful Shake-off and Armor Piercing would kick in. Of course, if you fail the roll you're just stuck.
Now, the question is can you use any of Rooftop to Rooftop without using all of it: can you not use L/C but still use the free move action.

edit: typing while talking to my wife about (her) work makes me slow: ninja'd by Q.

I don't see anything in Rooftop to Rooftop that would require the free move action to be an action that was used to activate Leap/Climb.

Same here.

So shake off + armor piercing + DC75th 052 Batman = poison lite? Sounds like I may have broken the game slightly... Oh well, now I see why feats are not used at many venues and don't come in boosters anymore. Thanks everyone for helping me puzzle out this highly situational and hilarious power combo.

I don't think the combo is that bad. If you want to deal damage with Shake Off you need to make a break away roll, which can fail. You will not be using Leap/Climb, so you may not be able to end up on the rim of elevated terrain to begin with - particularly not if Batman is occupying hindering terrain to make the most of his Stealth.
Also, I'd probably rule that if Batman fails his break away roll and thus does not end his movement next to the rim of elevated terrain, he would get an action token as the move action he took is not a free action.
So yeah, there's a lot that can go wrong with that plan.

Good enough.

Sorry over thinking things.