Are self-written statements/conditions between two parties legally binding?

No. Agreements written up between you regarding custody aren't legally binding in any real sense without a court order. However, if you are going to get a divorce it is possible to get a court order on child custody without any real "litigation". Whichever one of you files for the divorce can attach court forms laying out the custody/support that you want. They then serve those papers along with a blank response form to the other party. The other party then has 30 days to respond. If they agree with everything in the initial filing they can indicate that in the response form. You will have a hearing where the judge will ask about your agreement and make sure you both understand what you are asking for. If satisfied that you are, he will enter your agreement as a court order. As long as you are able to come to an agreement ahead of time and keep everything civil there's no reason that lawyers have to get involved. I would however suggest that you take your paperwork to the family law facilitator before filing it. They can help you make sure everything has been filled out correctly and explain any legal terms you are unfamiliar with.

I agree with Mr. Lofgren. Your agreement is not legally binding and can also have unintended consequences that you may not be aware of. The proceedings do not have to be contentious. If you both are in full agreement on all the terms, the process can proceed pretty quickly. Additionally, you would be well served to have an attorney draft your agreement to ensure that you are not missing anything and that it has the legal effect you both intend. The Facilitator's office in your county can provide free assistance in completing the forms and help you navigate the process. Be mindful that they cannot give you legal advice. Best of luck.

You and he can reach an agreement, either on your own, or with a mediator, but you will want and need, sooner or later, to make it into an enforceable court order. That doesn't mean "going to court to have a judge decide"; it means getting the agreement written into a formal document and filing it with the court.