Note, I am in the US, so my experience in both university and industry may be different than yours.
Is it advisable to finish the degree in Engineering? I still have all the credits previously earned. I'd take me a year and a half studying full time or three years doing it part time.
Definitely, absolutely not.
Only the highest degree matters. Having an additional bachelor's or master's does absolutely nothing for you in terms of qualifications. This is for a good reason: undergraduate degrees teach you "enough to be useful" in a professional scientific setting; a PhD teaches you how to perform research without supervision. The actual subject matter within STEM is largely irrelevant (perhaps modulo life science vs. physical science), since your actual job will require specific skills that you'll have to learn on the job.
Consider your opportunity cost. Even if this degree were useful, you would be sacrificing a lot of time and possibly money to pursue this. There are more useful things you could do, like throwing yourself full-force into your job.
Learn more about your 'real job' first. After you have a couple years of work experience and have settled on a particular career path / industry, you'll be better suited to judge if any particular classes or certifications would be useful.
Assuming I finish the degree in Engineering, how should I present it in a CV? Just the graduation date? The entire time span from starting date to finishing date like "from 2008 to 2020"? The time spans of the two phases like "from 2008 to 2011 and from 2019 to 2020"?
I would list just the year of completion. But this will raise eyebrows (people will wonder why in the world you have an undergraduate degree after a closely-related graduate one).
In the event of having a good postdoctoral opportunity with connections to the industry and real world applications, should I take it or should I start working in the private sector as soon as possible?
Don't do a post-doc if you're not aiming for a faculty job.
You may think a post-doc in academia is useful and fun. But eventually, you will start your 'real career', and you'll (eventually) find something that you also think is useful and fun. The earlier you start your real career, the more time you'll have to progress further and further.
Also consider your opportunity cost: doing a post-doc gives you zero additional qualifications relative to someone who didn't do a post-doc, outside of the particular niche area in which you did your post-doc. In contrast, a post-doc is a temporary position with a lot of uncertainty, very high expectations, and uncompetitive salaries.
The only reason you should even consider a post-doc is if you want a faculty job. Even if you do want a faculty job, most post-docs do not convert, so you need to have an honest assessment of what your odds are and whether it is worth it.
In short: the transition from university to industry is really jarring, especially given that all our role models are successful professors. It can be tempting to take temporary positions in academia rather than taking the leap. But it's better to get this over with so you can land on the other side. It might be bumpy to get established on a career trajectory you like, but once you do it, it is very rewarding to have a permanent position, a clear trajectory, and enough certainty about your career to start moving forward on other aspects of your life.
