fear on that head

Solution 1:

You're mistakenly grouping the word "fear" with the idiom "on that head", which is unrelated. The latter is a somewhat uncommon (although not unheard of) way of expressing "on that front", or "in that regard".

Your third example, for instance, is equivalent to:

I assured him he had nothing to fear in that regard.

Here are some examples of its usage decoupled from the word "fear":

• "... all sums due to and from the trustees of naval and military pensions previously to the period at which any payment from the Bank of England on that head ceased to be due ..." - (Mirror of Parliament)
• "He has not said enough on that head ; I know a great deal more of it ..." - (Mr Bayle's Historical and Critical Dictionary)