You don’t want/need a car in Edinburgh. Public transport is very good and parking a nightmare. Pick up the car when you leave.
When is this planned for?
That is an aggressive itinerary with long days spent driving. Distances may not look far but will take a lot longer to cover than you might expect. Driving in Scotland is slow. Plan on an average of 30-35 mph and don’t forget to factor in time for stops.
Day 3 - you are looking at 5+ hours just to do the drive.
One night on Skye - I do seriously have to ask if one night is worth the effort of driving to Skye. Most people recommend at least two nights and preferably three!
Day 5 is another full day drive. Depending on where you stay on Skye, you are looking at 7+ hours drive without any stops...
That itinerary would be too ambitious for me... You have just over three days from leaving Edinburgh to returning there and are trying to cram at least a full week into that time. Are you happy to see everything through the car windscreen?
What made you decide on this itinerary and what attracts you to Balmoral, Eileen Donan and the fairy pools?
Personally I would forget Inverness, Loch Ness (not one of the more scenic lochs) and Skye. Think about heading to Oban after Edinburgh and use that as your base. Do this as a circular drive via Callander, Crianllarich and Loch Awe. to Oban. Return via Lochgilphead, Inverary and Loch Lomond (or the reverse...)
Spend a day visiting Mull from Oban (equally as good as Skye) Another day drive up the coast to Glencoe and Glenfinnan viaduct.
Another alternative would be to head to Isle of Aran - easily reached by ferry from Ardrossan and spend the time there. This tends not to be on the tourist radar but is described as Scotland in miniature.