Hi, @Fátyol_Kristóf
For the main points, I think it would be best to refer to @lpb 's advice.
I will write below my personal opinion.
I believe that one of the good things about Asana is that each department and person in charge can use it freely. However, I think it’s best to avoid having each person work on similar projects in different formats. Using the template function is a good idea. I think that’s the correct advice. Although, ensuring its reliable execution can be quite time-consuming.
For point 2, I think it should be set automatically using the rules function.
Assign the person who registered the task to the person in charge, or perhaps the head of the department that registered it or the accounting person.
For the due date, you could set it to the day it was registered, or the end of the month.
I think it would be best to set the person in charge and the due date automatically, and then allow manual adjustments as needed.
For point 3, I recommend making everything a project.
I make everything a project: office administrative tasks, office schedules, weekly meetings, partner company lists, etc.
For point 4, set a filter in My Tasks to display tasks for, for example, this week and next week.
Alternatively, divide it into sections and use the rules function to assign it to a section (e.g., next month) based on the due date.
There is a lot of advice available from various sources regarding how to use My tasks.
Something like this, for example…