Officially, different major versions between GitLab and Runner are not supported. Even if it works most of the time.
I remember a long time ago there were some reports that pipeline were not starting when pushed to Gitlab and only when the commit was coming from the WebIDE editor. Your version of Gitlab is quite old, hard to investigate possible issues.
I suppose you see the commits in the project under Repository → Commits and they don’t have the Pipeline icon next to short SHA. This is usually when there are no valid Jobs according to rules or workflow.
Probably unrelated, but the rules in the provided .gitlab-ci.yml are set that unless you have a file in your repository which matches the value of $CI_COMMIT_REF_NAME those jobs won’t get executed ever (because exists is looking for a file). If you want to check if variable is present you just need to do:
job1:
rules:
- if: "$CI_COMMIT_REF_NAME"
Is the issue visible even if you have something really simple like?
stages:
- test
job1:
stage: test
script:
- echo "hello"