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mei/mei you is used is have have no so if i say ni you mei you peng yao i ask do you or do you not have friends.
hai is also so if i say wo de jia you mama baba hai you wo. my family has mom dad and also me
I'll give this a shot.
hái is used for more physical things that continue from the recent past. I personally use it when saying something like "he's still waiting for her to pick him up." in Chinese.
háishi is more used for habit or a long-term thing (and in my family, we use it for negative habits most prominently) as in "He still does not like to eat vegetables." --> Ta haishi bu xi huan chi ching cai.
I'm going to go on a limb here and interpret your méiyou - méi bit as asking about the two separately. finnegan might be right, that you mean you méi you , but I'll just give my answer.
méiyou and méi are very similar. I'm actually pretty sure that I've heard people use méi as an abbreviation of méiyou, as in "He has no food to eat"--> ta méi fan chi, as opposed to the longer (and I guess more grammatically correct) ta méi you fan chi.
I hope I could help you...and sorry if my pinyin isn't correct...I'm a native speaker, so pinyin isn't very easy for me. hehe... -.- I'll probably need to learn it someday. Everything here is from my own experiences and such, and I'm super sorry if it's not adhering to proper Putong hua. My parents both speak dialects of Mandarin (and very different dialects at that!) My dad speaks Teochu, the Chaozhou dialect (which is crazy different, so his mandarin pronunciation has a Teochu accent) and my mom speaks some Zhengzhou dialect where the inflections (that's what they are called, right?) are all different.
Well....sorry for my rambling, and for any non-standard things I might have claimed were in Mandarin. I hope this helps!