daimon you should be ok for a bit but 2 things I have to say.
1)if you install new flooring for repairs you will want to sand it down so that it is level and you have to sand the new pieces with fine grit even if it is already level with the rest of the floor or the finish you put down will look different on those pieces.
2)you can do the other floors first but if they are all connected just end on a seam maybe at a doorway where you will put a threshhold or something but it should be no big deal, I recently did a hallway with stain that joined 3 bedrooms with a natural look and it all looks good even with different colors.
Hope this info helps --after sanding and finishing some floors I realized it is not a precise science
1)sand with three different grits
2)clean up sawdust really good
3)stain (if you want)let dry 1 day
4)apply poly (1 coat per day)
5)buff
1 other tip: when staining or poly don't leave window open with sawdust on window sill, for example, as if the wind blows you now have sawdust imbedded in your finish