If I study to become a fashion designer is it possible people would buy my clothes online?I dont have connections.I just have a brain and ?

I would think so. With social media and influencers, it seems like it's easier than ever to sell fashions online.  Although it is best to also have an actual place where customers can come in to look, feel the fabrics, and try on.  Definitely get good sewing skills first.

You would need to know how to sew.  Etsy sells a lot of clothing. 

Sure. It's been done before. I know several who started on Etsy and moved to their own website once they established a customer base. Etsy is as good as any place to start. It's large, has an active customer base and it's easy to set up an attractive store site without knowing a single word of code.