I tried to pull up as many of the weeds (mostly baby weeds) to start out. After, I laid down the following layers in the exact order below:

1) Cardboard

2) Composted Cow Manure

3) Compost from my bin that wasn't done yet composting...mostly veggies mixed with leaves

4) Bark Mulch

I'm now worried that I was supposed to put an additional layer of composted cow manure on top of the compost from my bin (and below the bark mulch layer), so that it will be composted by April of next year.

My question is, will the compost "cook" or compost itself as I've laid it down?

Also, I currently have the area covered with a plastic garbage bag cut up to make just one layer...with stones keeping it down. This is just to prevent weeds from landing on my gardening area, as I have an absolute sea of them right now. Will this somehow prevent my layers from composting, since they're covered with that layer of plastic bag?

I hope I explained it well enough. :o(

Martha

That partially composted layer will be great for the soil.
It will attract & breed lots of worms that otherwise would not be attracted to or fed by finished compost.

Plant roots actually like growing into partially composted "organic chunks". Why people shift compost seems a mystery to me.

I've dug up vegetable roots many times to observe how they grow and they always attach themselves to twigs, branches, bark and any non-uniform organic chunks or even air pockets in the soil. The roots were always most vibrant in parts of the soil that were non-uniform.

Me, too.

Yes and mostly no.
If you bury a lot of vegetable matter together it will become anaerobic and smell quite bad, plant roots won't like that.

"Lumpy" partially composted is fine. I regularly do sheet composting, a well-accepted method, of kitchen scraps, it increases worm population considerably. The scrap layer is only about 2-3" thick with mulch (leaves, needles, or wood chips) placed on top. Ruth Stout was an early advocate of this method. The Lasagna method even advocates layers of uncomposted vegetable matter.

Some people even mix in kitchen scraps in their containers will good results.

With partially composted leaves, you probably heard it ties up nitrogen, which is true, but you can overcome that by simply applying more nitrogen fertilizer.

I've dug in large quantities of wood chips into my beds with great results. Many people say not to do this because it ties up nitrogen. But just two applications of fertilizer overcame this and my plants did the best in these "wood chip beds".

Check out my comments in the link below for an end-of-the-season update on this wood chip bed.