From left to right the medals he has are Iron Cross 2nd class 1870/71 campaign medal Bavarian 1866 campaign medal Bavarian long service cross (probably for 24 years of service) UNKNOWN
Based on this, he clearly served in two wars: the 1866 war between Austria and its allies (to include Bavaria) against Prussia and the 1870/71 war between Prussia (with its allies-including Bavaria) and France.
There is a Heinrich Funk shown in the 1877 list of Iron Cross receipients- he is the only one from a bavarian unit. Perhaps your relative went by more than one first name??
This man was an "Oberfeuerwerker" an artificer- someone responsible for ammunition, particularly artillery.
As far as dating the photo, it is most likely before 1895 when those individuals awarded the Iron Cross in 1870/71 were authorized to wear an oak leaf clasp on their Iron cross as well as attach small bars to their 1870/71 campaign medal showing which battles they fought in.
Perhaps if we knew what the last medal was, that might lead to a better dating, as it is most likely a commemorative of some description.