My first question is what is the better or more common and more usefull way to achive this
(what do most programmers prefer or find beter ) or does it not matter at all?
Most would use an ORM like Entity Framework, Nhibernate or even a micro ORM like Dapper. You can even use raw T-SQL with them as well. But you can also use straight up MYSQL Command objects and T-SQL too.
My second question is: lets say I have combined a couple of tables inside MySQL using for example LEFT JOIN clause
How do I use that combined table so I can use it in Asp net core and then send it to the client side.
A DTO travels and it's a data container object that can be used to shape the data that travels between the service and the client for CRUD operations with the database on the backend..
https://www.codeproject.com/Articles/1050468/Data-Transfer-Object-Design-Pattern-in-Csharp
asp net core reads the Products from the DbContext.cs That is able to get and send data in the database.
but how would that work with a Joined tabled Created in MySQL?
You would use a DTO to shape the data that is to be sent to the client, and on the flip side, if you send the data back to the service, the one must know the data that belongs to each table to be persisted to.
And since you are using .NET Core try to implement some of the below.
https://en.wikipedia.org/wiki/Separation_of_concerns
https://learn.microsoft.com/en-us/dotnet/architecture/modern-web-apps-azure/architectural-principles
Some like to use the generic repository pattern, I don't and I use the DAO pattern, becuase EF is already using the repository pattern.
https://www.thereformedprogrammer.net/is-the-repository-pattern-useful-with-entity-framework-core/
https://stackify.com/csharp-catch-all-exceptions/
Here is an example ASP.NET MVC client solution that is doing CRUD with a WebAPI using EF in the Data Access Layer (DAL) and the DTO pattern you can examine, which is implementing things talked about.