What @TomH said, but instead of the beam effect you can create another shape layer using the pen tool to create a line with just two points. Then use an expression to set the points on that path.
First create a null and put it at the starting point. Do the same for the end point, but parent the end null to the circle.
Now we'll create an expression for the ...
Importing stuff from Illustrator to AE is still a pain. Overlord is a good plugin that makes it a bit easier - it can transfer shapes to and from Illustrator. Also this script helps with putting selected objects in Illustrator onto their own layer.
If you want to move the end of a line around, you could make a null that follows the path of a circle.
Make a ...
Use constraints to do this:
Select the parent (the hand), then shift + select the child (the sword). Warning, selection order matters.
Rigging > Constraint > Parent Constraint > activate Maintain Offset if there's an offset between both pivot points.
Set a translation keyframe (shit + w) and a rotation keyframe (shift + e) on the sword.
By setting those ...
You can search "After Effects morphing" and you will find some tutorials which you will help to recreate intro like in this video. It's not a standart (by default) effect in After Effects. It's an animation created from scratch, probably in After Effects. It's a Shape Animation, shape morphing, mask morphing, liquid animation.
There are not that many options. "In general" (Sorry) you have
Change the origin point
So you simply combine them.
Then some images appear with spiral type spin/rotation
Change the origin point so it is not a rotation but a spiral
size change from small to normal
from small size to normal size with constant ...