I would like to know what's the best way to hide a squirrel trap so it is most effective. Also, how can I tell if there are baby squirrels in my attic? I'm afraid to go up there until I trap them all. Will the babies come out on their own or do I have to manually remove them? What time of day is best to go in my attic?

You can cover the trap with insulation or leaves. You should be able to hear the babies. If so, they will have to be removed by hand. Anytime is fine to go in, but approach the babies with caution. Mom will defend them.

I have squirrels (black) in my attic and have heard of companies that install a one-way gate over the animals' access hole, so they can come out but not get back in. I would like your opinion on this method and information about how to obtain such a device.

There is only one problem with such a device:
When locked out of their house, squirrels will almost always chew open a new door. To combat this, I recommend a live cage trap to remove them to a far away place. Then when the entry points are sealed, new squirrels will not have incentive to get inside.