A comprehensive list of human/mouse homologs is available from MGI at Jackson labs. This class report file is also useful.

It depends on what you mean by network function. I think it's quite reasonable to assume that orthologs are involved in the same biological process. In many cases, it can be shown that a human gene can rescue the loss of function phenotype of a mouse ortholog and vice versa.

Edit: corrected typo

Nope! You can cite it as evidence that they may play similar roles in human, but you should always proceed cautiously, even when moving between closely related mammalian species.