1. Put the cover of the manga on the list (like myanimelist.net)
   Since I search for manga and read them based on the cover (because when search for yaoi or yuri
   , I have to knew how the characters look like 🙂 )
   2.Advanced search by category
   For example you can search based on two categories. Or exclude one category from the search. (Again when search for yuri I have certain standards)

Quote from oneonezero

2.Advanced search by category
For example you can search based on two categories. Or exclude one category from the search. (Again when search for yuri I have certain standards)

As a matter of fact, you can search with multiple categories/tags at the same time. Just add the desired categories/tags in separate lines.
You can exclude a certain tag from your search by adding "-" in front of it.
E.g. if you want to exclude the tag "collection of stories" just type in "-collection of stories" (without the quotation marks)

For #2, in case you don't know where to find it, advanced search is located in genres. Just click "Genres" on the sidebar, and you'll see an "Advanced Search by Genre" link.

I think cover art would be difficult to implement in the search, especially because there are several series which don't have covers, or aren't allowed to include volume covers. (I also personally enjoy the cleanness of the interface right now.) And you could always just ask for recs if you want to know what the manga worth reading are.