An extension cable has a socket on its user end that is wired exactly as the house socket is, straight through (not parallel). Thus the active, neutral and earth connections are identical in position to the house socket. That is important.
The wire gauge used in the extension determines the maximum current that can be used on the extension end, and also length needs to be considered.
That maximum current is usually specified by the manufacturer, and is the recommended current not only that you should draw from the extension, but allows for the inevitable voltage drop along the extension to be within an acceptable range for most purposes the extension might be used for.
All conductors have an ohmic resistance, the larger the wire diameter the less resistance, the more current the wire can carry without undue heating and voltage drop.
The longer the extension, the larger the diameter of conductors needed to carry high current and have acceptable voltage drop at that current.
No, the house cannot compensate for losses in an extension.
Yes, more operating devices need more current and voltage drop will be greater.
Yes, it is POSSIBLE to compensate by use of a voltage transformer, but it is far more cost effective to have an extension with thicker conductors. In addition, if current beyond manufacturers' recommendations were used from an extension lead if you DID compensate, it will overheat, which makes the problem more severe, plus risk of fire.