a. John said Jane had given him less money than she actually had.
b. Tim said that Jim had dated fewer women than he actually had.
Are the above sentences grammatically correct?
a. John said Jane had given him less money than she actually had.
b. Tim said that Jim had dated fewer women than he actually had.
Are the above sentences grammatically correct?
Yes.
Whether you use "less" or "fewer" depends on whether you are talking about something that can be counted.
Obviously, women can be counted. You have one woman, two women, and so forth.
You might think that the expression should be "fewer money"; however, even though we say you're "counting money", you're actually counting pennies, nickels, dimes, and dollars, and adding up the value of them to find the amount of money you have. You would never say you have "four money", so money is not considered countable in this sense. Thus, you have "less money."
Note that this distinction is becoming less common in American English; using "less" in both cases is very slowly becoming more common. (As an example, the express lines in grocery stores often say "10 items or less.")