I make changes in .cs files and also some changes with the designer. After this I compile and run the project.
The problem is that it shows the my old form, and it does not show the new changes I made in the form.
In other words, I don't see the changes I made when I run my application.
Try to Rebuild or Clean/Rebuild project, of course first be sure that you Build it after change.
When you have compilation errors and stuff like that Visual Studio will pop up a windows asking if you want to run the last successful build. It has a checkbox that says "Do not show this dialog again". If you have previously checked that box it can produce something like what you are talking about.
This may not be your problem but at the very least you should check it out, just in case.
The window looks like this:
To fix it go to your Tools->Options then: 
I don't think it is a problem, you may not building the application.
I would check your Configuration Manager for your solution. It's possible that your active solution (e.g. the solution type specified by your Configuration / Platform combination) is not set to actually build the project.
The Configuration Manager has a Build column with checkboxes. Ensure that all the projects you want to build for a configuration are set to build.
