Wood – How to fix particle board at lock screw (Ikea Effektiv)

You don't wish to retain the lazy susan/turntable?

Then it's fairly simple to turn that into storage space, some of which will be difficult to access (which is why people often accept the LS/T losses of potential space.)

If there's no side next to the stove, you'll need to make one. If there is, you just need to make some shelves, and screw supports for those shelves into the cabinet sides and the wall studs.

You can either paint the drywall or overlay it with plywood depending how much you care what the inside of the "cabinet" looks like.

As for supporting the concrete top, there's two stages to that - if you are pouring it in place, that's the tricky time and you need to provide adequate support (temporarily) to keep the heavy wet concrete from sagging on whatever you use as a bottom form, as well as enough reinforcing that it will support itself when cured. If you are pouring and curing it separately, then installing it, you only need to hold it up when cured, and that can be more cleats (robust ones) on the walls, and perhaps a diagonal brace across the corner.

It would help to know exactly what you want to accomplish because there's likely a better finishing method than stain in your situation. A good first step is a paste wood filler to smooth out the surface imperfections. You may need to shop around a bit or online, and it's helpful to decide on a finish first.

Paint is the easiest solution, any you have some flexibility with sheen and texture if you open your options to chalk and milk paint. That being said, many people don't care for painted furniture and "stain" is often a code word for wanting a clear topcoat which is problematic with paint.

Lacquer is much more common than paint for factory finishes. It's not brush friendly but you can buy it in spray cans. On its own you'll get a durable fingernail polish type of finish, while preserving the option of adding a clear lacquer topcoat.

For problem pieces a gel stain is a much better option than stain conditioner. They're thicker than conventional stains so they don't absorb unequally. The advantage for you would be the ability to apply polyurethane as a topcoat. It's also much more rag and brush friendly than lacquer.