From Illinois Newbie

Hello Everyone,

So glad I found this forum. I have been reading everything I can on gardening and my head is about to explode. I live in the Chicago area and have just started working on my first organic garden. I found videos on a no-dig garden and finished that about 2 weeks ago. I would like to get started planting so I can have a harvest in the fall. I am mostly interested in planting vegetables and need some direction. With the Illinois climate I am wondering the following:

1). What should I be planting right now?

2). Can I plant potatoes from ones that I can cut up?

3). Sorry if this one is stupid, but am I able to take frozen organic broccoli and plant from that?

The seeds I currently have are:

Green Beans
Watermelon
Parsley
Tomatoes
Sunflower
Spinach
Cucumer
Carrots
Oregano
Cabbage

I would truly appreciate any help the experts could give me, I am committed to try and make this work.