make the surface smooth and remove the dust and bubbles if any.
No, with water, the quick drying time, the lack of collection of dust as much, you just might run over it with a light sanding by hand and go.
But, if you do not want to sand and don't mind the slightly gritty finish at first, then you do not have to. The foot trafic would sand it down quick enough.
I would not go over the first coat with the mixed stain treatment, I would use clear only. I cannot see where the stain would work over already stained areas.
This would surely get a seal and stain quicker than using oil.
Go to a home center and read about it and see the samples.
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