I guess you're aware it's the festival in Edinburgh through August? As a result it's very very busy and accommodation can be difficult to find and very expensive, so best to book something asap! It would seem natural to split your trip 7 and 7, but I wouldnt necessarily stay a full 7 days in Edinburgh -There is a fair bit to see, but it's a medium sized city (around 500k) so I think 3-4 nights there is enough - and if you're not there specifically for the festival you may start to tire of the crowds in some areas. As a result you could maybe stay somewhere else in Scotland for a few days.
Edinburgh isnt necessarily great base for visiting many parts of the Highlands as it's simply not that close to them. There are day tours to the Highlands that get good reviews, but they involve a lot of time sitting on a bus due to the distance. You can travel to/from/around the Highlands by train - there are scenic lines like the W highland line from Glasgow-Mallaig etc so that may be an option. I guess it depends how much you want of the natural settings. Trips from Edinburgh that are easier are St Andrews and Stirling by train and maybe trips out to local sites like Rosslyn.
If you're interested in museums and cultural sites you should probably visit Glasgow. You can do it as a day trip by train from Edinburgh as it's is 50mins away by very frequent train service - but there is more to see than can be managed in a day so given your interests I'd probably stay a night or 2. It also has better access to much of the Highlands so you could perhaps do a a day trip from there to somewhere like Loch Lomond and take a sail on the Loch or take a trip from there on the W highland line.
I'm not sure why your highlighting "regional" airline? KLM operate several flights per day from Edinburgh (and Glasgow) to AMS and afaik the vast majority of flights are operated by KLM mainline with Boeing 737 series aircraft, their regional subsidiary cittyhopper rarely appear on these routes. Easyjet also offer both routes with Airbus A319s rather than regional jets.