stovewood
I am thinking about closing the hole that you see on the picture below using wood. The metal sheet will be screwed onto the wood "frame" that I would be building. Is it safe to use wood? The stove pipe never gets too hot, I can touch it with my bare hands but I'm still a little bit concerned.
The wood won't touch the pipe, only the metal sheet will.
You took the wind out of my sails with that last paragraph. I was going to suggest using a nut/bolt.
As far as it causing problems when the tabletop is lowered, you can recess the bolt head. Yeah, you could make the cavity in which the bolt will stay on the underside of the tabletop, but maybe you'll drill too far or crack/scratch the tabletop if you chisel it out. It could end badly... which is why you should instead house the bolt head on the top-side of the cross member.
Brown = table top
Black = underlying cross member
The one on the left is what you were talking about. The one on the right is what you want to do.
Also, use a washer under the bolt head, etc.
To add stability you could use 2x6 members for the cross pieces along the bottom. Then cover the bottom with a half of a sheet of plywood. Pour concrete into the box thus formed at the base by the 2x6's and plywood.
You could get by without having to go all the way to full angle braces across the sides (which would get in the way of your hanging plants anyway) by installing some gussets made of thin plywood as shown below:
At a suitable size these would probably come right up to where the first hanging pot wires go.
I see that you have each corner made of just one 2x4. I would encourage you to make the corners out of two 2x4's attached in an L shape in each corner. This will go a long ways toward making the unit a good bit sturdier and will also make the cross bars on two of the sides have a whole lot more wood to bolt into.
I would echo that the proper fasteners for this structure are going to be 1/4" or 5/16" diameter carriage bolts as opposed to screws or nails.
Best Answer
Depends on what the manufacturers specifications say.
For the particular doublewall insulated chimney (not "stovepipe" which is singlewall) I last had to work with, clearance to combustables was 2" from the pipe wall. The deformations at the joint appear to be consistent with what you have being double or triple wall insulated chimney, not stovepipe.
Stovepipe (singlewall) typically needs at least 18" clearance to combustibles, as it may get red-hot in the event of an excessive fire in the stove, or a chimney fire in the pipe.
Since the part shown is intended for framing support it's typically safe to have wood where the sheet screws in for support.
But the manufacturers specs (for the exact pipe and accessories you are actually working with) is what rules. You can almost certainly find out who that is by carefully examining the pipes (the info will be stamped into every piece, in my experience.) Then you should be able to look up the installation manual for the pipe and support piece.