From Battlestations Rulings 14 August 2005

Any action that would cause a module to become used (pumping engines, launching missiles, etc) will still cause the module to become used if the action fails. (Power will still be spent, as well) [YG 132] Modules are color coded indicating the primary skill used in that module.

Modules can be repaired from any space in the module (p38). Anyone assisting can be anywhere in the module (or outside the module, adjacent to the player fixing it. [FAQ]

In general, you can operate any battlestation remotely (with the -3 penalty). You must be local for some actions:

1. Converting a cannon (cannon)
2. Repairing a module (Any)
3. Putting out a plasma fire (Any)
4. Being teleported (Teleporter)

When operating modules remotely, the target module gets used markers normally (and these cause penalties or prevent actions normally). The module you are in does not get used markers, and you ignore any used markers it already has. [FAQ]

Those little numbers (1-6) in the modules are used for when people teleport (p54) or arrive via boarding missile (p51). Or anything else that randomly appears.