Visa validity

I am Japanese language student and my graduation in on 15th of March 2019 but my student visa expires on 13th of May. I am planning to work 28hours until 31st of March and leave japan by first week of April. Are we allowed to work after the graduation?

And there is another scenario I am stuck with, I have applied for working visa and I am not sure whether I will get the visa or not, but until I am notified about the visa, am I allowed to stay in Japan and continue working for 28 hours? Staying here without a work is a big trouble, life becomes hard without work in japan. Your little help will be highly appreciated.

I am Japanese language student and my graduation in on 15th of March 2019 but my student visa expires on 13th of May. I am planning to work 28hours until 31st of March and leave japan by first week of April. Are we allowed to work after the graduation?

As long you are participation a school, you can work. If you finished your study and you finished school, 0 you must need to inform immigration with in 2 weeks about your change.
So technically you should be fine with work as long you school has not informed immigration that you finished you study.

And there is another scenario I am stuck with, I have applied for working visa and I am not sure whether I will get the visa or not, but until I am notified about the visa, am I allowed to stay in Japan and continue working for 28 hours? Staying here without a work is a big trouble, life becomes hard without work in japan. Your little help will be highly appreciated.

After you finish your study you need to inform immigration about your status ( see above).
You can stay in Japan as long you are in the process for you work visa but you cannot work since you do not have the proper visa. You need to wait till you get the correct visa.

You can work 28 hours until 15th March.
You can stay as long as your application is in process.

from customary interpretation,
if you graduate on March 15 (graduation ceremony is held on that day), you are treated as a student until March 31.

when you work with a student status, you must be a student. i.e. you can work until March 31.
after April 1, you are not a student. you can't work, even though you have a student status and a permission of work.

You should really actually read the text of your "work permit", as it specifies the conditions attached to it. If you don't read it, how do you know that you are abiding by those conditions and not working illegally?