I have several questions concerning school.

Should school be plural or singular?

elementary school is from grade 1 to grade 6
elementary schools are from grade 1 to grade 6

Second question,

Which one is the correct way to count grades?

from grade 1 to grade 6
from the first grade to the sixth grade
from first grade to sixth grade

When is it necessary to use the in front of grade

for example which one is correct?

I'm in the first grade
I'm in first grade

Third question,

If I say school levels,in the plural, does it refer to levels such as grade 1, 2 ,3, 4 etc; or, levels in different schools or different places.