How can I make a basket out if regular brown rope? Can it be sewn?

It can be sewn if you have a very large needle and strong hands. I would try finding a container the shape you like and wrap the rope around it gluing the rope to itself (not the container) as you wrap it, continuing to wrap it ending with a coil to form the bottom.

consider using hot glue it really has a strong hold

What you are wanting is a coiled basket. Do some googling and you should find instructions. It is very easy and no glue to worry about and very nice projects. Easy and fun and creative. On a quick search I found instructions and a video on utube. Have fun.