I was just wondering if there is a very simple way to move all of the transformations and masks within a layer.
you could select the keyframes and do this manually. press U to reveal show properties with keyframes and rectangle select them with your mouse. then move. if you want to move the keyframes forward in time by precise measurement there are also shortcuts:
if you are looking for something else, you may found it here:
if you still need help, try to describe exactly with the aid of screenshots what you want to happen and maybe we can offer a solution.
These are my most common techniques for finding and adjusting the position of keyframes in a comp.
To reveal all of the keyframes (or expressions) in a timeline deselect all layers and press the u key once. Pressing the u key twice reveals all modified properties for all layers.
To reveal all of the keyframes on specific layers select the layer, or shift select to select a range of layers, or Ctrl/Cmnd plus click to select specific layers and press the u key to reveal keyframes or the u key twice to reveal all modified properties.
Selected layers may be moved in the timeline along with all of their keyframes by clicking and holding on one of the layers in the selection and then dragging left or right.
Selecting the Anchor Point / Pan Behind tool (y) and clicking on a layer in the time line and dragging will keep the layer and all of it's keyframes in the same position in the timeline but roll the in and out point of any movie or nested comp in that layer backwards and forwards in time. Did you follow that? The keyframes don't change, the start and end times for the movie in the timeline don't change, but the edited in and out points for the clip change. It's called a rolling edit.
To reposition a group of keyframes in time you can drag a selection around the so they are all highlighted and then click and drag on the group to move them all at the same time without changing the in and out point of the layer.
To reposition all keyframes for a modified any modified property you can select the property in the timeline to select all keyframes and then drag them left or right to change the timing of all keyframes.
To proportionally change the timing of a series of keyframes you can drag a selection around them or select all of them then hold down the Alt/Option key and drag the first or last keyframe to proportionally change the time of all keyframes.
As Roei said, you can use the Alt/Option or Shift + Alt/Option and the left or right arrow key to shift keyframes right or left 1 frame or 10 frames at a time.
With the most recent versions of AE:
While an animation is previewing you can double click a keyframe and edit the values in the pop up window without stopping the animation.
While an animation is previewing you can manually adjust the values in the timeline by dragging to set a new keyframe at the position of the CTI.
While an animation is playing, or any time you can use the j or k key to jump the CTI to the previous or next revealed keyframe, marker, in point or out point of any layer in the timeline.
While an animation i playing you can set the in and out point of selected layers at the current playback time by using the Alt/Option + [ or ] .
My most used technique for a group of keyframes is the drag a selection around them and then hold down the Alt/Option key and proportionally drag the first or last keyframe to change the timing of the animation (the move that took 3 seconds now takes 1), and my second most often used technique for a group of keyframes is to select them all and click on one to drag the entire group left or right.
I set and use markers all the time to make it easier to time my animations.
I hope these techniques help you work more efficiently.
I should mention that if you can reveal motion paths in the timeline or in the layer panel for anchor points or effects that are not visible in the Composition Panel you can also drag a selection around them or select that property in the timeline to select all visible keyframes, and then reposition all of them at once by clicking and dragging on just one of them. This is another technique that I use all the time.