If you have to redraw your logo in Motion, this might help:
https://youtu.be/SXUFGZqF6h4
It's fast and reduces errors.
To move points in the Canvas, select one (or more), hold down the Command key and type the arrow keys to go 1 pixel at a time or the Command and Shift keys to move 10 pixels. You can type in values for individual points if you go to the Shape Inspector and you might have to reveal the Control Points section if it's not showing by double clicking on "Control Points".
You will not have access to the tangent line control points only the main points on the line/shape.
You can animate ALL the points with keyframes on "Control Points" in the Shape Inspector (not the individual shape points) or you can use the Record button (I always forget to turn it off again, so I don't usually recommend this method). A keyframe "node" will reveal itself when you mouse over the Control Points label "bar" in the inspector.
I recommend that if you are animating the shape, start at the point at which the most points required are used, then manage their locations over the course of the animation. I do not recommend attempting to add or remove points for an animation.
You can animate from any point in time forwards and backwards - once the initial keyframe is set since it is just a matter of moving the playhead and making adjustments to the shape (as soon as a change is applied, Motion automatically sets a keyframe in place.)
HTH