A contour interval is the difference in elevation between two contour lines. It has nothing to do with the distance on the map. So it is not related to the scale of the map.
One topographic map uses only one specified contour interval. Different map could use different C.I.. The common C.I. used in USGS topographic map is 20 ft for map of 1:24,000 scale.
Contour line usually use even number as its value. For example, if a map has C.I. of 50 ft, instead of given contour lime values as 132, 182, 232, etc. they should use values as 100, 150, 200, etc.
Not every contour line is labeled with a value. With a known C.I. and a single value, we can count and find out the value of unlabeled lines if we can identify whether it should increase or decrease in value.
Elevation at position outside a contour line is not known for sure. However, it is bounded by the elevation of the two adjacent contour lines. For example, everywhere in between the line of 3500 ft and the line of 4000 ft has elevation in between 3500 ft and 4000 ft. It could be 3502 ft, 3560 ft, 3989 ft etc.