Making a game is hard, and I don’t have vast experience to show off and search for a job.
But I can contribute to the engine at my own pace without pressure.
Apart from the “Betas and Experimental” part, how can I contribute and learn about Unity engine along the way?
You can file bug reports for any issues you encounter.
Various parts of the engine are open-source, too. Take a look through the Unity-Technologies repositories on Github, at the active ones - for example, our fork of Mono is there. (Please do check the contribution instructions on any repository before digging into them, though - we cannot accept pull requests on some of them).
And of course, there is the asset store.
If only Unity would allow us to fix their asset store. 
And where can I find your git repositories along with the opensource ones?
Theese: Unity Technologies · GitHub ?
Yep, those are the ones. I think we have a few on Bitbucket too, but we’re moving everything over to Github.
Ok. There are 210 repos related to Unity3d. Which one do you think its best to start?
Or which one needs more work?
If your purpose is enriching portfolio related to Unity and doing real contribution, crafting an editor asset and promote it in store is the best way.
However, nitpick the source and make pull request to call it contribute is not. Interviewer would criticise your total time and effort in any reference. If you want to a short cut, a crappy homemade game or skillset demo is weighting more than short term contribute.
From your words, you may be quite talented, wish you good luck in job hunting.
It really depends on what sort of thing you’re interested in. If you’re into graphics, you might want to dig through the ShaderGraph and PostProcessing repositories. If you like animation, the SimpleAnimation component might be a good one, etc.
Just make sure you read the CONTRIBUTIONS.md file in a repository before starting anything!
I would like to start with writing docs for the simple animation project. What do you think, does it need docs?
If yes, is there some page for documenting c# code in unity3d? Or do the standard c# guidelines apply?
I think we don’t have a page up about that yet, but the way things are going with the new package system, I think XMLDoc comments is the right way to do it. Assuming that the SimpleAnimation component is converted to a package at some point (which it probably will be), XMLDoc is the format that the API docs will need to be written in.
However, you should probably raise this question as an Issue in that repository, rather than here. Let me know when you’ve done that and I’ll go make sure the animation team have seen it. 
Are we talking about Node js plugin xmldoc - npm
or this MSDN class XmlDocument Class (System.Xml) | Microsoft Learn ?
