Planking: Your wood veneer is old. The adhesive used to bond the top layer of veneer is old. It needs to be glued/bonded on again.

This is not the cheapest way to fix planking but I wanted wavy, planked cabinet sides locked down tight. Because it was a cabinet with both sides planked I had to get serious. I bought a large 8 oz. bottle of super glue. I laid the cab on its side and flooded the side with light viscosity fast setting superglue. The super glue flows under the planked areas and bonds everything super tight and it will never plank again. Then I did a light sanding, applied any Bondo to smooth things out, sanded again and then painted.

EDIT: I should add that I used one 8 oz. bottle of superglue per each cabinet side. At $27.00 a bottle, the fix was $54.00. But it stays fixed and is cheaper than a new cab.

CAUTION: If you do the super glue flood method, either make very sure you have enough fresh air or wear a mask. Super glue in quantity will knock you on your butt.

Broken cab corners: You have gotten many good suggestions.

I prefer to get out my wood chisels and cut the broken wood away, then bond on a piece of replacement veneer. Some hobby shops sell veneer in different sizes and thicknesses. Some stores like Menards sell veneer. Home Depot of Lowes might sell veneer, but I am not very sure.

If you have a friend with a table saw, a piece of 2 x4 can be cut into various thickness of veneer. If it is a small repair area you can use a popsicle stick or tongue depressor ( a box of 100 depressors costs $1.00 at Dollar General ).

If you go the resin route, try to get some fiberglass cloth. Start cutting the cloth into short small pieces like hair (the smaller the better). Mix these small pieces of fiberglass into your resin. Resin by itself does not have much strength but with glass hairs mixed in it is almost bullet proof.

You do not need to remove all of the paint. Some of the best surface for new paint adhesion is old paint. However, with the cabs I have been repairing/restoring I fail to follow my own advise and sand them to bare wood.

If you are sanding by hand, just bite the bullet and go buy a vibrating sander. A Google search shows you have all kinds of pawn shops around you. Try to get one with a hook and loop style sanding pad. Don't get some pee-wad size palm sander. Get a larger size sander for the big jobs.

This sander will work for smaller jobs and tight places. But if you get something similar then you can buy your sanding media at Harbor Freight and save a little money. Abrasives are not cheap.

You will most likely find all styles of sanders in the pawn shops.

I start with 80 grit and then move to 220 grit sand paper and then move to 320 and then 400.

I am not endorsing this particular sander but these types of sanding pads are hook and loop style.

https://www.amazon.com/Enertwist-13000OPM-Lightweight-Polishing-Decoration/dp/B07CSDT2PG

I would ask the shop that is going to mix up your custom color paint for you.