Why is it not "donnés" as "nous" is plural?
The direct object of "donné" is "un nouvel espoir." The indirect object of "donné" is nous.
Agreement when using "avoir" is only for the direct object that precedes the verb.
Why not Votre étudiants...?
The noun is plural, so you need "vos" instead of "votre".
Why étudients and not éleves
Both "étudiants" and "élèves" are accepted here.