If the Quest card has a the Battle or Siege keyword, but the players choose a side quest without keywords as the main quest, do still abilities such as that of the Southron Company (Southron Company gets +2 and +2 while the current quest card has the battle or siege keyword.) still apply?

22 minutes ago, Yepesnopes said:

If the Quest card has a the Battle or Siege keyword, but the players choose a side quest without keywords as the main quest, do still abilities such as that of the Southron Company (Southron Company gets +2 and +2 while the current quest card has the battle or siege keyword.) still apply?

In the case of Southron Company, the ability does not apply while the side quest is current.

But remember: side quests can generally only be "current" during the quest phase, as the rules revert the current quest to the main quest during other phases. So you can't use a side quest to debuff the Southron Company's attack during the combat phase.