I don't think Zhanchi or Weilong are among the most used cubes any more. I'd say the most popular cubes right now are Aolong v2, Gans 356, Yuxin and probably Meiying. Don't now about Mats but yes, Feliks 5.66, at least one of them, was done with a white Zhanchi. More recently he changed to an Aolong v1 (that got him the [in]famous 5.33 DNF corner twist), then a Gans 357 and latest that I know of is the Gans 356, I think. He's probably used other cubes in between but I don't think he used a Weilong, at least not for long and not recently.
Regarding best areas of each cube a long article could be written on that subject matter. You have plenty of video reviews and blog entries where you can find information about that, unless you have a more specific question that can be shortly answered.
Yes and no. Define what you mean by outdated. Recently Feliks did a comparison of several cubes, new and old and he said he was surprised to realize how good the Zhanchi still was (I think he got times that were second only to the Gans 356). If outdated means they went commercial years ago then yes. If outdated means they are really bad compared with newer cubes then only marginally or outright no. I am barely sub-20 with the best cube out there, while Feliks was sub-6 with a Zhanchi. I have a Zhanchi and a Weilong and many other newer cubes like Aolong v1, Yuxin, Yueying, 357... and I don't think there's that much of a difference between them if correctly set up. Which one I use as my main is just a question of preference but I have used as mains at least 4 or 5 different cubes and when I have them set up to my liking and I have enough time with them to be confortable, my times are very similar with most of them.
Sometimes I think, oh my new main is so great because I average this or that and my old main was bad because I averaged 1.5sec slower. Then I try my old main and I discover it's not the cube but me. I'm improving and now I can easily beat my old times with my old main and get averages close to those of my new main.