Hi nhrdls, you questions are good ones and reflect the searchs you have made. Good on you. As you will come to realize, there is no single right way and very few wrong ways to compost. My opinions are.
(1) What you suggest with the solar oven will likly kill many seeds but avoiding weeds that have matured to seed might save labor and browns in the form of paper and cardboard are easy to find.
(2) I think the majority of those who microwave do so to speed up breaking the food down . Freezing access food for later use serves double duty,stockpileing food plus causing faster breaking down. I wouldn't reccomend the solar oven because I don't think it adds value and might actualy dehydrate and extend time required for it to rot.
(3) Ahh,finaly something I have actualy done several times. Doing as you describe imo avoids some heat generated as the food starts to decay. I'm in Tx and I notice you are in zone 9 where summer temps are high to begain with. BTW posting your zone will help those answering your questions and giving advice. In addition to "staging food" in the compost bin I often seed near finished compost with worms if the compost is to be stored for later use.
I would like to suggest a composting arangement I believe well suited to adding material to a small bin at regular intervals. Construct your bin so a spade or fork can remove material on one side at ground level. Occasionaly pull material from the bottom and place it on top. That alows checking progress,airating the bin and seeing if moisture,brown or green % needs reduced/increased.

The USDA's Plant Hardiness Zone means little. It was devised to give people some idea of what plants would survive an average winter in their area and nothing more. A general description, such as "West Central Michigan", would provide more and better information necessary to provide good advice.
A solar oven may work since I have baked a Cherry pie in one in the past, but you will need to monitor what is going on since you could start a fire quite easily.
Compost bins need a certain volume to achieve the heat, produced by bacterial activity, necessary to kill off those "weed" seeds and undesirable pathogens. Just placing a pile of organic matter in the sun in the hope that will work just is not going to, although here a solar oven may since that will concentrate the suns rays.

My compost pile also may not get that hot so I just avoid putting in items that I think would not be good there, including weeds with flowers and seeds. If I get the weed young enough, I will go ahead and put it in the pile.

I also avoid even using sticks and small branches because my pile doesn't decompose them fast enough for my uses.

So you can add many things to your pile that you haven't thought about, but you don't have to add everything that you think about.

i painted the top of my compost bin black, and have it somewhat angled toward the sun

New Orleans is normally much warmer than it is right now
its like 65-70 outside. -Normally its 80+ for the beginning of May

I will take the extra few degrees.
i would hate to have to go buy 3-4 bags of compost when i can get better stuff in a week from now, since it appears almost ready to use.

"So you can add many things to your pile that you haven't thought about, but you don't have to add everything that you think about."

That's a profound statment but I'll bet someone has tried anything you can name at least once. At any rate I like the message.

As a general rule the sun has little to do with getting a compost pile heating up and painting the bin black does nothing to change that.. If the composter built a solar array that might help some, because then the suns rays would be more concentrated, but it is still bacterial activity that generates the heat most people look for during the composting process.
Where sunlight does play a role is in helping the plants that will be composted grow.