We had an almost identical situation in a former garage that we refinished to be an office. Our contractor suggested this and we liked the result: he installed a piece of wood about an inch out from the concrete, putting insulation between them and keeping the wood a consistent and level height - a little higher than the concrete. I can't remember if it was pink fluffy insulation or spray stuff. Then a shelf about 6 inches out from the wall - nice and level by being a bit up from the concrete and supported by the vertical wood, and there's insulation under the shelf too. The whole thing is a good looking clear pine and is well varnished.
Looking from the side gives an idea of the distance from the wall:
The shelf runs around the entire room and is remarkably useful for something so low. It hides all the lumpy bumpy aspects of the concrete and while it's not something you see everywhere, no-one has ever mentioned it so it can't be that unusual.
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 really should remove the stuff that was mixed overly wet - that tends to make cement products very weak. As a result, it should be easy to remove - might even come out with a stiff broom, if not, stiff wire brush might well do it.
Check the labelling on your paint - in most cases you should wait at least 30 days before painting (or attempting to paint) any fresh concrete product.