This reponse has been updated to reflect changes to SG7 in the November 1 Game Manual Update.
Please also consider the "red box" in rule SG7, partially quoted here for reference:
Other than a situation involving a blatantly intentional Violation of <G14>, any Robot which is in Possession of more than three Discs is in Violation of this rule, regardless of intent, circumstance, or context.
As well as the Violation Notes for rule SG7, partially quoted here for reference:
Egregious Violations, such as continuing to play other portions of the Game (e.g., Rollers or Endgame) without attempting to remove excess Discs for the majority of the Match, or "accidentally” Possessing an egregious amount of Discs, may also be considered Major Violations at the Head Referee’s discretion.
The use of the term "egregious" is intended to imply that a Violation does not need to be Match Affecting in order to be considered a Major Violation. Therefore, an egregious Violation during a Robot Skills Challenge Match could still be considered a Major Violation.
With that in mind, regarding your specific questions:
Assuming a robot possesses a fourth disk in a skills driver run and the driver does not attempt to remove said disk until his or her robot is lined up to score in a goal, are they in violation of <SG7>
Yes, as this describes a Robot which has continued to the play the game, and did not immediately stop all actions and remove the fourth Disc. A Robot that does not succeed in removing excess Discs during the Match cannot continue to play other portions of the game, as described in the 2nd violation note of rule <SG7>. A Robot that is in violation of rule <SG7> cannot participate in further gameplay and will not receive points for tiles Covered in the Endgame. If a Robot successfully removes the excess Discs, they may resume playing other portions of the game.
If so, is how will the team be penalized for the violation?
If the Head Referee determines that the Violation was egregious, then it would be considered a Major Violation, and therefore a Disqualification.
If, during the skills autonomous period, a robot unintentionally possesses more than three disks and waits until it was lined in to score in a goal before removing any excess disks, is the robot's respective team in violation of <SG7>? If so, is how will the team be penalized for the violation?
The answer to this is the same as above. G11, quoted below and partially bolded for emphasis, states that Teams are still responsible for the actions of their Robots during the Autonomous Period (or the Programming Skills Challenge).
<G11> All rules still apply in the Autonomous Period. Teams are responsible for the actions of their Robots at all times, including during the Autonomous Period. Any Violations committed during the Autonomous Period that affect the outcome of the Autonomous Bonus - whether they are Match Affecting or not - will result in the Autonomous Bonus being automatically awarded to the opposing Alliance. If both Alliances commit Violations during the Autonomous Period that would have affected the outcome of the Autonomous Bonus, then no Autonomous Bonus will be awarded.