Are commander mana abilities usable without my commander being on the battlefield? Ex: Sliver Overlord as my Commander.
They are not. The only special properties of a commander are when it dies you can return it to the command zone, and that it exists in the command zone and can be cast from there. Of course, like all other magic, there are exceptions {Oloro, ageless ascetic}.
Oh god imagine Arcum using his ability from the command zone.
In general, an ability will only work on the battlefield. There are quite a few exceptions to this rule of thumb, but in most cases, either logic dictates or it says so: {Oloro, ageless astetic} says: when in the command zone etc.
An example of logic: cannot be countered functions on the stack, since it would be useless otherwise. (A spell can only be countered while on the stack)
{derevi, empyrial tactician}.