Nope! Another great thing about Sea-Monkeys, they will not eat/attack the eggs or the young Sea-Monkeys.
They all live together in relative peace :-)
The only "trouble" that occurs is the males fighting over a female. But you must leave them to it.

Most people would tell you no. Just to use the Sea-Monkeys million bubble air pump or something similiar.
For a regular size tank, such as the ocean zoon tank, an aquarium air pump is not suitable.
Although, if you clamp/use a valve for your air pump, just to let a few bubbles come through, then this would be fine.
I wouldn't recommend an air pump soley for your Sea-Monkeys tank though. If you are already running an air pump
to your fish tnak etc. then you could add an extra connection to it for your Sea-Monkeys as just the smallest amount of
air flow is needed.

The real problem though is the weight of the air stone/air tubing knocking your tank over!
If you can secure that, then sure, great :-)
Just make sure the air flow is a steady stream that isn't too "violent" on the water. You want the water relatively peaceful in your tank.
Too much air and the baby eggs will be floating all over your tank all day along with the babies.
Personally, I would use a manual pump once daily, but it is possible with an air pump, just not that practical.

You can get another container and pass the water back and fourth a few times.
I can't say I'm a big fan of this though.
Alternatively, you can use a "pipette".
A pipette (also called a pipet, pipettor or chemical dropper) is a laboratory instrument used to transport a measured volume of liquid.
For the price of a million bubble air pump, you cna probably get around 40 pipettes!
A little slower to use, you have to insert it into your tank, squeeze to release the oxygen/bubbles, now, don't "un-squeeze" yet
as this will suck up the water, you don't want to do that.
Raise the pipette out of the water, then let it fill back up with oxygen. Lower it back in and repeat the process around 5 times.

This will do the same as the million bubble air pump, just at a slower pace.

Cutting the end of a pipette (as it widens the further you go up) will also create an "aqua-leash" for sucking up things.