you shouldn't need to cover it, it will rot, and in the winter you shouldn't have to worry about it drying out.
covering it will make it anerobic, you're looking for aerobic activity.
it really doesn't matter how you put stuff into the bed, but it would break down faster if you did cover it up a lil with the other stuff in the bed.

Thanks!

I should have said cover up temporarily -- in the book I read it said she sometimes covers up with black plastic for a couple of weeks to start it heating up.
But I guess that is optional so I won't bother about it then.

(Sorry for all the typos)

Yes, you can add your peelings or anything else you want right up to planting.

The hardwood mulch is a bit of a problem because I presume you want to keep it on top. If so, you will have to brush it aside to add your layers.

You can scrounge all kinds of things for your layers---coffee grounds from Starbucks, sometimes leftover produce from the grocery, your household leftovers.

It's sounds like you're off to a great start.

I cover mine with burlap. Read about interbay mulch in the FAQ. It discusses burlap. Also I found that critters like to dig for veggie scraps in my lasagna bed so I just stick to UCGs and finished compost for my sources of nitrogen.