Errors in module-info.java
Even if the compliance level of the project has been set to Java9, there might be shown misleading errors for module-info.java in Eclipse. 
I expected that an update of the maven project would only be required if I change the pom.xml file. Now I learned that changing the module-info.java also requires a manual update of the maven project.
=> update the maven project (Alt+F5) 
After that update my errors vanished. 
I also learned that it is better to first update the versions in the pom.xml file and then generate the module-info.java. Otherwise the module-info.java will include non-existing modules like "requires log4j" instead of "requires log4j.api"
Another misleading error in module-info.java might occur due to pom packaging, see below.
Unresolved imports
For the case that an import can not be resolved the question might be "Which corresponding (new) module do I need for that (old) import?". What might help here:
- Search at following page for the required page:
http://cr.openjdk.java.net/~mr/jigsaw/ea/module-summary.html
(lists all exported packages of the JDK-modules) 
- Use JDeps on the (old) *.jar file to get a list of required jar files, e.g. - jdeps --class-path "lib" -recursive MY-OLD.jar  >output.txt 
- Use jar to find the module for a jar file - jar --describe-module --file REQUIRED-JAR-FILE.jar 
Also see:
Re-Export dependencies
In order to automatically make log4j visible for a grandparent project
grandparent => parent => log4j
you might want to use 
requires transitive log4j.api 
in parent instead of
requires log4j.api
in grandparent. Also see:
What's the difference between requires and requires transitive statements in Java 9 module declaration
POM packaging
My main issue seems to be that my Java8 pom.xml file used pom packaging:
<packaging>pom</packaging>
If I remove that line, no errors are shown in module-info.java
Also see this extra question: How to use maven with Java9.0.1 and pom packaging in Eclipse Oxygen 1a Release (4.7.1a)?
New log4j version
A. In addition to the change "requires log4j" => "requires log4j.api" I had to adapt the calling code for the new log4j version that is compatible to Java9:
private static Logger sysLog = Logger.getLogger(Main.class);
to
private static Logger sysLog = LogManager.getLogger(Main.class);
B. log4j 2 does not have PropertyConfigurator. Also see this related question: 
PropertyConfigurator in log4j2
C. log4j 2 does not support log4j.properties files. Previously I used  
src/main/resources/META-INF/log4j.properties
for configuration. Now I use
src/main/resources/log4j2.xml
Also see 
Working example as a reference

pom.xml:
<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
  <modelVersion>4.0.0</modelVersion>
  <groupId>Log4JWithJava9</groupId>
  <artifactId>Log4JWithJava9</artifactId>
  <version>0.0.1-SNAPSHOT</version>
  <build>
    <sourceDirectory>src</sourceDirectory>
    <plugins>
      <plugin>
        <artifactId>maven-compiler-plugin</artifactId>
        <version>3.7.0</version>
        <configuration>
          <release>9</release>
        </configuration>
      </plugin>
    </plugins>
  </build>
  <dependencies>
  <dependency>
            <groupId>org.apache.logging.log4j</groupId>
            <artifactId>log4j-api</artifactId>
            <version>2.9.1</version>
          </dependency>
          <dependency>
            <groupId>org.apache.logging.log4j</groupId>
            <artifactId>log4j-core</artifactId>
            <version>2.9.1</version>
          </dependency>
  </dependencies>
</project>
module-info.java:
module Log4JWithJava9 {
    requires javafx.base;
    requires log4j.api; 
}
Main.java:
import org.apache.logging.log4j.LogManager;
import org.apache.logging.log4j.Logger;
public class Main {
    private static Logger sysLog = LogManager.getLogger(Main.class);
    public static void main(String[] args) {
    }
}
Eclipse plugins
In order to add log4j to an eclipse plugin, I copied the file log4j-api-2.10.0.jar in a folder "lib" and added the jar file to Java Build Path=>Libraries=>ModulePath
Instead of requires log4j.api I had to use requires org.apache.logging.log4j
