Torn/Chip Drywall/paint (pics) help!!

How would you repair this?

1) I took off a wooden panel , and this was underneath it, do you suggest to do a Mud or spackle?



2) I had to cut a hole in my textured ceiling, not sure how to go and repair the hole

 

Insert a board into the ceiling. Cut it long enough so it will extend past the edges of the hole. Screw the board from under side of drywall. Now you have an area to screw in the small piece of drywall for your patch.
Before inserting board, place a screw in the middle of the board, facing down.
This is a handle for pulling down on board while you're inserting the edge screws.
You can then tape and mud patch. Mud just a little at a time, applying several layers to get the best look. You can texture with an aerosol can or try to match with a sponge.
The drywall with paper torn will require a primer, such as Gardz. Gardz does the best job of adhering any torn paper edges, and prevents the paper from bubbling up when mud is applied.

 

Brian said it well

You could use an oil base primer instead of Zinnser's Gardz, that's what we used prior to Gardz and still use on occasion.

almost forgot welcome to the forums!

 

Spackles used to fill tiny nail holes.
If your going to use new base that's going to cover that area there's no reason to take the time to fill those low areas.