You can buy proper weed barrier at most hardware and garden centers, it sold on a roll and looks like a fine mesh fabric.
yes, it should work, there are mulch films that are black plastic that I put out under my above ground container garden. it works very nicely. if you use a clear type, cover it well.
It is about the same. I put down some 6 mil plastic about 15 years ago and secured with rocks around my HVAC unit. It has worked great but I wish I had overlapped a bit more.
You certainly can, but over time your mulch may mold if moisture does not evaporate.
No, because the plastic will keep water from percing (draining) into the ground. Instead, use landscape barrier fabric, which you can buy at the garden center. It has tiny holes or openings to allow water to drain through.
I have used black garbage bags before and it worked great! Just make sure to poke holes in the plastic for water drainage otherwise it will get moldy and ruin your soil