Do you think that people would trust me if I show them some of the codes that I have made or it would be necessary to do some courses to obtain certification ?
You might be having a lot of certificates, but in the workplace world, showing them to a potential company/academia would not probably land you the job/course directly because it is the due diligence for certificates and/or interview for your knowledge as mentioned in those aformentioned certificates.
Certificates issued by reputed institutions could be of some value to a few recruiters because it lessens the efforts to test the candidate knowledge to an extent. Otherwise nowadays, most recruiters value what you have worked on and their models and results/observations. You could put it up in code-hosting sites like github, gitlab, sourceforge or your blogs.
Certificate is not a must unless mentioned by companies/universities. For instance, GMAT, IELTS, GRE, TOEFL and/or LSAT scores are made mandatory by most of universities for foreign students (and/or local students).
If you are confident and able to learn on your pace and comfort, then by all means, do it on your own. If you have doubts, then as you wrote in your question, you get help by using SO community and with your friends.
Could be a good Idea to do a posdoc related in bioinformatics or data science ?
Data science prepares you for any field that involves understanding and dealing with data whereas bioinformatics is more specialized form i.e data science + biology (dealing with biological data). But bioinformatics should also help you to transition to another field of informatics like astronomy or marketing.
Either way should help you for a career in data science.
That said, you need to see the reason to do postdoc. For most cases, PhD should be enough. So, you need to see whether doing postdoc would leave impressions on your career prospects.