You're Correct!

The arms play an important role in the golf swing working alongside the shoulder rotation to lead the club on the best possible arc for a good angle of attack into the ball, but their movement is a relatively complex one.

During the back swing, the left arm should remain as straight as possible but not so firm that the wrists cant hinge whilst the right arm bends to inside 90 degrees. During the down swing, the wrists will start to unhinge as the right arm becomes straighter, then at impact the left arm will still be straight with the right arm just starting to straighten. On the follow through, the roles are reversed and the right arms extends towards the target whilst the left arms bends.

Both arms during the swing straighten and bend but do not remain too stiff otherwise the length of swing in particular will be hindered.

To practise and figure out the tension in the arms for yourself, use half swings and get your back swing to the L position with a straight left arm, bent right arm and hinged wrists. Then swing through impact to create a mirrored view on the follow through. This will help you figure out how much the arms move and you can feel the tension in them during the swing. Also, you will gain invaluable practice of the 9 oclock pitch shot which should be used on the golf course also!

If both arms are rigid throughout the swing then the right arm in particular will not bend on the back swing causing a shortened swing with potentially no wrist hinge, resulting in a shallow angle of attack and an array of bad shots. Allow the wrists and arms to move throughout the swing for lasting consistency in your swing

This is correct to an extent because you do want them to be loose enough to move correctly, however, if they are too loose then both arms will potentially bend causing a narrow top of the back swing which will then lack power through impact.

If the right arm stays rigid throughout the swing it will make the right arm more dominant through the swing meaning the tension through the arm will go all the way to the wrists and prevent any hinge from taking place and shortening the back swing. The implication of this is a huge loss of distance due to a slower swing speed through impact but also, an array of poor strikes due to the shallow angle of attack.