The Past Tense for the "gave" is here because of the weird grammar rules of the English language. For some reason it forces us to use the tense as well as to use things like "were" in phrases like "I wish he were a Superhero". It's called an "imaginary wish" (a wish that can't come true). You can use "I wish he be a Superhero" for a wish that can come true, aka "real wish". So, since you have used the past tense, you are trying to say something that you believe can't happen in fact. For such things in Russian we have "я бы хотел" (past tense + бы) with possible options like "Как бы я хотел", "Я хотел бы", etc. Pay attention that the "бы" is necessary to convey the impossibility. For theoretically possible things we have a few options without "бы" like "Я хочу", "Я желаю", etc. Both of them need "чтобы" and something in the past tense, something that you wish were or be going to happen, depending on what modality you are trying to use.I wish my school gave
Here are a few examples:
Я бы хотел чтобы моя школа развалилась и мне не пришлось ходить на занятия (unreal wish)
Как бы я хотел, чтобы мама принесла мне новую игрушку. (pay attention that the verbs look as if they have happened, complete past, perfective)
Как бы я хотел, чтобы мама приносила мне по новой игрушке каждый день. (Past imperfective, every day, a series of actions in the past)
Well, here is the classic:
Как бы я хотел, чтобы ты стала моей. (I wish you were mine)
Я бы хотел чтобы ты стала моей.
Я хочу быть/стать космонавтом (I wish I be a cosmonaut) - real wish, short variant (without Чтобы), only for "be", "become" and "have" (быть, стать, иметь); works for unreal wishes too (Я бы хотел стать космонавтом).
Я бы хотел иметь 20 млн. рублей. (Я бы хотел, чтобы у меня было 20 млн рублей)
Okay, now you can see that the correct option for this subjunctive stuff should be "Я бы хотел чтобы + моя школа давала/дала". Actually it's давала because you don't want it to give the lesson once, you would like that it would give the lessons e.g. twice a week 9 months a year or something. So we have the correct thing "Я бы хотел чтобы моя школа давала..."
Класс для русского языка is okay but it means "a classroom that is okay to conduct Russian lessons". Since you want actually lessons, not a classroom, you would want to use "уроки", not "класс". Actually "класс" can also be okay for a class like "класс фортепиано" but "уроки" is much easier to use and not so tricky so I do recommend that you use it. The trick for a "класс X" is that you have something huge/massive/not detacheable, some kind of special equipment installed in the classroom needed to conduct the lessons so this class(room) is assigned or specially designed for a specific lesson. That's about a "класс" vs "lesson".
Something like: Уроки фехтования состоятся в классе фехтования.
You need genitive with "уроки" like "урок математики", "он приходит на уроки русского язка с опозданием", "он не любит ходить на урок физики"...
Now, the word "давать". In Russian you can hear "давать уроки" for private tution, not for public education. A school or an institution can HAVE a class (specific lessons) in Russian. Actually it looks like "в нашей школе есть урок математики" or "в нашем университете отменили уроки английского языка".
So you can compile the sentence:
Как бы я хотел, чтобы в нашей школе были уроки русского языка.
Hope that helps.
P.S. Note that the "unreal wish" stuff with "бы" CAN be used for real wishes in the same way you use "would" for polite requests like "I would like 65 cups of coffee", "Я бы хотел 65 чашечек кофе -> а вам дурно не будет, сэр?"...