Have you studied the Subjunctive yet? #1 requires the Subjunctive if y ou say what is wanted. Queremos que nuestros hijos tengan maestros buenos y competentes.
2. Esto requiere que el gobierno no gaste más dinero. I don't know what you have there but the sentence should say: "This requires the government to not spend/waste more money.
If you have NOT had the Subjunctive, I'll have a LOT to tell you about it!
3. with worry, you need the Subjunctive = I wouldn't use "El" but "Lo que me preocupa es que no tengamos suficiente dinero."
4. Es importante is NOT something that requires "a" before an infinitive, although there are verbs/expressions that DO! Es importante trabajar más en la escuela.
5. difference between "quien" and "que" = Esta es la chica que no sabe condu cir.
6. By the way, you are learning NOTHING if you don't try these sentences first. We HELP here but do not DO the work for you. I am only doing this because the Subjunctive IS tricky at first. What you need is a good explanation of why it exists in the first place. Unfortunately, it is dying out in English ! But not in Spanish, or French, for that matter.
Los estudiantes deben aprender que es posible graduarse sin trabajar. (deber & es posible do NOT take "a" and after a preposition ("sin") the only form of a verb you can have is an infinitive.
7. No para = Sería ridículo tirar todas las reglas a la basura. (throw AT, vs throw IN = tirar...en )