Your best bet for a good finish relies on doing three things:
- Making sure that the foundation for the extension is well compacted and onto good material
- Cut back and scable the joint with the existing 10x10 slab so that there is a good bond when the new concrete is cast.
- Drill and fix dowel bars into the existing slab across the joint with the extension.
The number and type of bars will vary depending on the load from the new shed but you should be fine with something like 8mm (3/8") bars at 200mm (8") centres.
You should probably note that this will give you a full structural connection and so may be too much for your particular problem unless you want to be absolutely sure that the slab and the extension don't separate.
There are (at least) two different types of stains for concrete. One is a surface coating, the other is acid etching.
The former can work, but isn't as durable/lasting. I believe most of the products you get at the big-box stores are more of a top-coat type of stain.
Acid etching is just that, it's a stain containing an acid that actually etches the concrete. This is the typical type of stain you see in home magazines and such. The etching provides a deeper stain that is more durable and not prone to flaking.
I've done the latter, and applying it is super-easy. It's the prep work that can be a chore--namely if you have adhesive on the concrete already. In our case, we has tile mastic, which we had to dissolve using soybean based stripper. It worked great but was incredibly messy.
If you don't have glue to deal with, however, you should be good to go. Order up the stain (lots of places online to get it). You then dilute it per instructions and spray it on the concrete. I used a garden sprayer for this. You then let it sit for a period of time, and then you apply a neutralizer to stop the reaction.
After that, you apply water and mop/squeegee/wet-vac it up.
Then, you apply a sealer of some sorts. Common options are wax-based, polyurethane, and epoxy. I went with poly as it was relatively easy to apply (roll it on). That said, I don't think it was ever truly waterproof. For your needs, you may want to go the epoxy route.
Best Answer
You can lay laminate over the concrete with only the prescribed pad.
Some manufacturers recommend a 5mm combination pad and vapor barrier. Others recommend nothing. Check as to what is prefered for your flooring.
In my location 90% of the homes have concrete slab floors. A vapor barrier is not needed for a floating floor, but can be used as an additional pad if allowed.
There probably was no need to grind your floor. Simple scraping of the glue should have been enough. ( there is a misconception that a subfloor has to be glass top smooth and flat to lay LVP or laminate. It doesn't)
If you wish to cut down the dust from the ground concrete, you can spray or roll on a sealer/ waterproofer. Allow to dry and start your floor project.