Hello your site is currently using bootstrap, that's good because that web framework brings a slider that meets one of their requests ("the slideshow need work on mobile"), then it is to reduce the height it is something simple to do and the last part not visualize very well ("need the slideshow to part 4 parts (Search 3 Hot deals block and slide block"), if you can do a little expansion I sure thought propose an appropriate solution.
I'm working on a demo from the browser on your website, the show in awhile.