Quick and Easy Questions (please read the OP)

[Trixie]

If someone successfully raided your base, could they use the base's extensions against the owner's will (so long of course as nobody is around to stop them), for example the DV Uplink or Healing Station?

It depends entirely on the condition of the base once the assault is completed. See the Rules Page for Assaulting Bases. 

http://omniverse-rpg.com/fights.php#Assaulting_Bases

An excerpt: 

Depending on the damage done to the base during an assault, it may take weeks to restore its integrity. During this time, artefacts may be unable to be securely stored there, and certain base improvements may be unusable (determined after the conclusion of the assault). Alternately, you may pay 500 OM to repair it immediately.