Feasibility of obtaining an “individual doctorate” in Germany while working?
Um, I had to google "Individual Doctorate" since I wasn't sure what the German was supposed to be, but apparently this is just the default way to do a PhD in Germany? In which case:


Yes. When I was a PhD student in Germany, the only documents required by the university administration were the B.Sc. and M.Sc. transcripts/diplomas and a letter from my advisor stating "I am supervising this student". There was no selection, everyone who handed those in was enrolled.
Yes, but only if the company agrees. (As @Wolfgang Bangerth notes, many companies will not allow you to divulge details about the work, as they are basically their trade secrets.) Note that in Germany theses have to be officially published, so the "jury is under NDA" workaround that exists in other countries cannot be used.
It is feasible, but the success rate is much lower than for PhD students. I don't know anyone who worked at a private company, but we had close contact with a Fraunhofer institute group, and even for employees of a research institute who had that option explicitly planned for in their employment contact, many of them gave up along the way. The work required for an actual, useful product is very different from research (e.g. there is nothing novel about making sure I/O works correctly for a wide variety of formats, so you are likely to get scooped by some full-time PhD student who is just duct taping five scripts together and copy-pasted the input data into their source file).