Are modern newspaper inks a health risk?
Before anybody may wrap some food in a newspaper, it needs to be printed.

Given that workers in print shops are the first that are exposed to potentially dangerous compounds, this is a matter occupational safety their national regulations.

In Germany, the BG ETEM provides an extensive exclusion list for inks and solvents. Compounds covered by this list are not be be used!

In order to avoid an endless recital of compound names or CAS numbers, the exclusion list is based of GHS hazard statements and includes (among others):


materials with CMR properties:
H340, H341, H350, H350i, H351, H360, H360F, H360D, H360FD, H360Fd, H360Df
materials with specific organ toxicity, acute toxicity and other health risks:
H370, H372, H300, H310, H330, H301, H311, H331, EUH 029, EUH 031, EUH 032


Summary

Does this mean that German newspaper are safe for handle in production and daily use? Yes, unless printing houses violate existing regulations.

Is the same true for Indian newspapers? I have no idea, since I am not familiar with the legal situation in India.