The exact rules and implementation of stopovers varies a bit between airlines. I don't know the KLM specific answer, but at a high level the answer is the same for most airlines.
In general, you pay the same price for the airfare, plus the extra for the stopover. However there can be cases where the airfare will go up due to the addition of the stopover.
Airlines break fares down into multiple "buckets", and then control availability on each flight based on those buckets. Certain flights may not have specific buckets available, and as the flights are priced based on these buckets, there may be no "cheap" seats available on those flights. The number of seats in the cheaper buckets varies based on things like the number of tickets that have been sold, and the day of the week the flight is on (eg, the cheapest seats might only be available on a Tuesday!)
When booking a stopover, you normally need the same fare bucket to be available on both legs of the flights. So say you're looking at flights on a Tuesday (cheap seats available!), but then add a stopover for a few days and depart the stopover city on a Friday (no cheap seats!) - then the total price will go up. In fact, you'll normally end up paying the higher fare for both legs of the flight. Plus you'll still pay the $75 for the stopover!
No, Minimum stay doesn't apply for stopover - but you'll still have the original minimum stay requirement (if any) at the destination point. ie, 3 days at the destination and 2 at a stopover point does NOT meet the requirements for a 4 day minimum stay.
Generally the best way to book is to use the "Multi-City" search on the airlines website (or a 3rd party website), and list the stopover city as one of your legs. eg, if you're flying AAA-BBB via AMS and want a stopover in AMS, then enter this as two legs in the search - AAA-AMS on one date, and AMS-BBB a few days later. The website will look after pricing this correctly, including any stopover fees and working out the lowest fare buckets available.
Note that sometimes the fare you'll end up with won't be a single fare with a stopover. Sometimes it's actually cheaper to book two separate fares (eg, one from AAA-AMS, the second from AMS-BBB). If this is the case it'll automatically be handled by the booking engine so you don't need to specifically worry about it.