removing /category/ from the URLs

Hi my category URLs appear thus

http://www.domain.com/category/cars/volkswagen/

I want to remove the word “category” making it look like
http://www.domain.com/cars/volkswagen/

I HAD put in the word “category” in Permalinks settings > Category base. I deleted it and all my category URLs still appear with the word “category” in them.

I also wanted to change the Permalink structure for Posts so I put in
/posts/%postname%/

and I found that the category URLs are now appearing as
http://www.domain.com/posts/category/cars/volkswagen/

I want the category URLs to be like
http://www.domain.com/cars/volkswagen/

and the post URLs to be like
http://www.domain.com/posts/%post-name%/

Please explain me how to get this done. I am also thinking of instlaling the super cache plugin whether it would produce html pages for category pages too.

I also want the tag pages to be like
http://www.domain.com/tags/food/

But the “tags” display does not appear at all in my blog page. I am using SIMPLA theme and I guess the theme author has not put the code to display tags. I would prefer something like a tag cloud to display on every blog page with the most-used tags. Can somebody point me in the right direction? Do I have to hack the simpla theme files to build tags support on my own?