I have several projects for which I enter new fix-version in a regular weekly pattern. Can a script generate new fix-versions?
Yes, have a look at com.atlassian.jira.project.version.VersionManager#createVersion, eg
import com.atlassian.jira.component.ComponentAccessor
def projectManager = ComponentAccessor.getProjectManager()
def project = projectManager.getProjectObjByKey("ABC")
def versionManager = ComponentAccessor.getVersionManager()
versionManager.createVersion("1.1", new Date() + 7, "the description", project.id, null)
I regularly do this as part of my release process using JIRA Command Line Interface using addVersion . Similarly for releasing versions.
You can do this from a command line script using the JCLI client or if you use Confluence, it can be easier using CLI Plugin for Confluence and a page like:

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