You can pray with shica's if they are zayidis and ashari's(twevelers) so long as they don't talk bad about the sahaba and our mothers. Also, the only takbir (Allahu akbar) that is wajib in the salat is the first one Takbirat Al Ihram.
Advo, they are not praying to rocks I don't know why you would some ignorant stuff like that c'mon guy, but in their methodology they have to pray on pure earth, and some say clay, and they have their own ahadiths for that.

