For instance if I put up a staircase that will need to be rescaled. Rather than resizing it manually, is there an easy way to tell Core to resize it for me such that the top and bottom ends of the staircase align with the second and first floors respectively?
Not currently. There are a couple ways to get things scaled appropriately.
First, you can hit R and use the scaling tools. I don't often find it useful to have snap on, so make sure you have it off unless you determine you need it (G key). For finer tuning on scales you can hover your mouse just to the left of the X, Y, or Z scale fields in an Object's property. You'll see a horizontal arrow with 2 heads, left click and drag and you'll change the number in the respective field by small increments.
Also, if you are doing it multiple times, you can use templates. Or you can copy the properties of the object that has the right scale using these buttons to copy and paste.
If you are just going for scale you can right click on the Scale label in the properties window to copy and paste scales like this