Will cells from different species have the same structures and functions?
Generally speaking, yes. The closer 2 species are evolutionarily, the more structures and functions they will have in common. For example, it would be next to impossible to tell the difference between human cells and cells of an ape or, in most cases, even another mammal. Probably, for most cell types, it would be difficult to tell the difference between a human cell and a chicken or iguana cell. Even if you could tell the difference, most of the stuctures and functions are the same. Even with plant cells, which are visibly different from animal cells even to a layman, most of the structures and functions are the same. As we start comparing bacteria and archean cells to our eukaryote cells, we would see more differences, but still some similarities.