Enquiring PI about post-acceptance process of admission (PhD, Germany)
Should I mail PI requesting to let me know the status as some of the official things were halted (like visa application) from my side? 


Yes (assuming that you are polite). In most, if not all, German science institutions, the administration is a separate department. It is very unlikely that your PI sympathises with them and in fact, most scientists in Germany I know are not on very good terms with their administration.

Moreover, your PI is much better equipped to spur your administration than you (and everybody else for that manner):


Its his research project that is delayed and possibly also his funds that are wasted.¹
He is usually higher-ranking than than the people handling your employment, though not their direct superior.
He is usually experienced with that specific administration.
He knows all the details of the process, because he started it.


Finally, he usually has an interest in things going smoothly for you. If your PI exhibits no interest in taking care of these matters, you should reconsider your decision to take this job.

The only exception from this may be if your PI’s group has its own secretary. Then it’s the secretary’s job to deal with such things and they are the best person to talk to.


  Generally how much time HR people will take to send this information to the candidates?


Administrations in Germany can strongly differ in efficiency, usually depending on their backlog. I did experience such a process to take longer than a month, but that was by an administration that has a nation-wide fame for its incompetency. Still, most administrations are capable of handling things quickly, if they want and need to – maybe they just failed to notice that you need a confirmation of your contract early for visa affairs.

However, there are certain inevitable durations. For example, depending on the circumstances, your employment may have to be ratified by some personnel board, which only meets at certain intervals.



¹ If all things fail, he can threaten to report himself to the authorities for wasting tax money.