MBP 13 early 2015, but battery was manufactured at November 2016. Why?
No, I do not believe this is suspicious. The early-2015 model 13" MBP is still a current model. So, unless you actually bought the MBP before November 2016, this is not at all suspicious.

To put your mind at ease you can check your MBP's serial number at a number of sites to retrieve the manufacturing date amongst other info. You can access one such site here.

[EDIT]

In response to question update. 

The fact your serial number search shows it was built in either Week 24 (June) or week 51 (December) backs up my assertion. This is a new MBP built in December 2016 (after the manufacture of your battery and before you purchased it).

This confirms there is absolutely nothing suspicious about your MBP.