Is it true that Newton ordered the hanging of counterfeiters?
No.
The counterfeiters were tried in a court of law, with a judge presiding, were found guilty by a jury and sentenced by the judge according to the penalties set out in law by parliament.
The role of Newton in these trials was primarily to obtain evidence and witnesses of the counterfeiters' crimes.
The Wikipedia Article on William Chaloner citing a biography by Paul Hopkins and Stuart Handley says:
The trial was held at the Old Bailey on 3 March, the Judge was Sir Salathiel Lovell
...
Newton fielded eight witnesses that spanned Chaloner's career. Catherine Coffey, wife of goldsmith Patrick Coffey, declared that she had seen him coin French Pistoles. Elizabeth Holloway declared how Chaloner had bribed her husband, the coiner Thomas Holloway, to flee to Scotland and avoid giving evidence at the 1697 trial. Thomas Taylor the engraver in the major coining conspiracy. Catherine Carter, wife of Thomas Carter who had twice previously been named and blamed by Chaloner, testified to Chaloner's skill as a forger and his role in the lottery scam
...
The jury needed only a few minutes to reach a verdict, and he was sentenced the next day.
Is this true?
No
Newton did not order any executions, nor could he.
How many men did he hang and over what period?
None
Did his measures work?
Partly,
Chaloner ceased to counterfeit currency.
Counterfeiting is today still a problem.