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I would wait at least 30 days for the concrete to dry very well. That way the stain will seep into the pores of the concrete better and stick
If the weather is keeping the concrete wet, then wait until you have a couple of weeks where the weather stay dry.
Berh makes some very good concrete stain and sealers that you can actually have tinted to better meet the color you may like.
What I do is apply a coating of the stain and let it dry.
Then with a pump sprayer, I take the same stain and thin it down a bit, and then use the sprayer to apply more of the stain to different areas to give the look light and dark stone. You can do this several times and each time it will get a little darker where the coating is several layers deep.
And as far as some relief cuts in the concrete? Yes? No? What are your thoughts on that?