When an Entropic Vault or Cold Vault would be powered by an Energy Core they override the energy core effect. This doesn’t mean the vault is active but instead simply that it can’t be activated by only the Energy Core or Generator. Negative effects override positive effects. If an Energy Core would be active and is connected to a Cold or Entropic Vault that is also properly activated through connections the Cold or Entropic Vault overrides the Energy Core and deactives it.
Yes and no. Once a Link has been connected it instantly activates. If the card is then left alone and nothing changes, the Link can't be activated again. However, if you manipulate the cards in question in some sort of way, for example by swapping the room that activates the with another room that can also activate the link, you may use that link effect again.
