when was the peak period of the ivory hunting?
(when a man could make a living out of it, and before licenses, cites permits, etc.)

Prior to 1910 based on the books I have read on the subject. However, it depends on the country. Ethiopia was the last place that 100lb tusks were routinely taken (if you can call it routine). Most of the big tuskers were taken by British hunters in the late 1800's early 1900's. There were commercial hunters, not sport hunters.

There have been plenty of big elephants taken up until the various countries cut ties with European countries.

That pretty much covers it. The big time ivory hunting ended for the most part with the closing of the Lado in 1908 or 1910, I forget which.

It's not really an easy question to answer and it depends at least partly on how you view it.

As Will & Dogcat say, thing changed a lot after the Lado closed..... until then, it must have been pretty free wheeling and after that, a small amount of control was introduced. Ken Stewart and the Lemmer family for example, remember times much later than 1910 when they used to shoot elephants and deposit the tusks in the bank as credit. - During those times, it was normal to only shoot an Elephant if you thought it was 100 lbs a side or bigger. If I remember correctly, (and I may not!) Ken told me the licence cost (£10) and allowed for 3 Elephants.

If you search hard enough here, you should find some old photos........ I'll also dig round and see if I have some pics of the period. I get a vague idea I have some Lemmer pics on one of our computers for some reason...........

FWIW, I have a buddy who lives up the road who used to be one of the biggest ivory dealers in the business and some of his pictures of tusks warrant a second and third look. Admittedly, most of his purchases were from various GDs and Govts.