Because it's actually shorthand for a more formal sentence, such as "Mi donas saluton al vi." ("I give a greeting to you.")
Since the greeting is the direct object (it's what's being given), it's in the accusative case.
The subject is 'mi', and 'vi' is the indirect object (as indicated by the preposition 'al').
No, Saluto is incorrect. You may find this guide on when the use the -n ending helpful: