Use 4 to 6 inches of mulch only.

Here is a link that might be useful: Growing asparagus

can we grow Asparagus in Alabama? and when do we grow it?

Landscape fabric is a bad joke. If you think you need something under the mulch, use newspaper. It will not cause a nightmare in your future. Asparagus clumps do grow, leave them some room to get bigger. The newspaper may take a couple years to fully decompose and new shoots could have trouble breaking through it next year.

Does asparagus need full sun all day in zone 7b or could I plant it in a spot sheltered from afternoon sun from 3:00 p.m. on?

Sure you can grow asparagus in Alabama. Just watch out for the asparagus beetles, they can destroy a bed in no time at all. Pick them off or, if you don't mind pesticides, sprinkle with Seven Dust. You're supposed to plant in early spring but we had some crowns that we didn't get in the ground as early as we should have so we went ahead and planted them about a month ago. We'll see how they do, especially in this heat and drought.