from my English textbook

●Corporal punishment is a form of punishment of school students for misbehavior. This involves striking the student a given number of hits or whips either with the use of rattan cane, a wooden paddle, slipper, leather strap or a wooden yardstick.


the student a given number of hits → the student given a number of hits


●The use by schools of corporal punishment has historically been covered by the common law doctrine of loco parentis.


The use by schools of corporal punishment → The use of school corporal punishment


I think there are two corrections needed like above. Or original sentences are correct?

The original sentences are correct.

● "This involves striking the student a given number of hits..."
This "given" is not the same as the "given" in your re-written phrase. "Given" here means something like "particular."
It could be re-phrased like this:
"This involves striking the student a particular number of hits..."
or
"This involves striking the student a certain number of hits..."

● "The use by schools of corporal punishment has historically been covered by the common law doctrine of loco parentis."
This means that the "loco parentis" law doctrine covers corporal punishment when it is used by schools. "Corporal punishment" is a compound noun but "school corporal punishment" doesn't really work as a noun phrase. It's more natural to say "the use of corporal punishment by schools" than to try to say "school corporal punishment."