Gradle version and gradle-wrapper.properties

How do I download the latest Gradle version automatically within a Android project? Do I manually change the file gradle/wrapper/gradle-wrapper.properties

Yes.
You have to change the gradle/wrapper/gradle-wrapper.properties

For example:

distributionUrl=https\://services.gradle.org/distributions/gradle-2.5-all.zip

Then, sync the project. Android Studio will download the new version automatically.

And change 2.4 to 2.6 and run gradlew?

First, sync the project.

When I create a Android project, why is not 2.6 there from start?

The new project is based on a template file.
For this reason, currently any new project is with 2.4 version.

You can change the template, but AS will update it with the next updates.