Latin diphthongs

Can there be diphthongs spanning root and case ending, i.e., are meus and meum one syllable words while mea is a two syllable word?
Also, can there be diphthongs where one or both vowels are long? Take for example the genitive of meus, mei (long i). How would that be pronounced?

>are meus and meum one syllable words

No, they're two syllables, at least under British/American pronunciation.  (A different system of Latin pronunciation is taught in Continental Europe, which I am not familiar with.)