You may not want to take tours, but in some cases they will be the most reasonable and efficient way to see the things you have on you list.
This is true especially if you are not used to driving on the left side of the road in a car with the driver's seat on the right.
In general, I'd say the places you want to go are spread out and that the travel time to get to them by any means of transportation is longer than you might expect. Some may not be easily reachable by car, or indeed reachable at all except by a tour.
Keep in mind that 2 nights in a location really only gives you 1 full day there. I spent 4 nights in Kirkwall on Orkney and still didn't see all I wanted to see.
I took a Northlink ferry from Scrabster to Stromness and a public bus from there to Kirkwall. I flew from Kirkwall back to Aberdeen. The Northlink Ferries websight I linked has lots of tourist information along with transportation routes and timetables.
While in Kirkwall, I took a day tour to see all the sites you have on your Orkney list and more. I found the tour at the Tourist Information office in Kirkwall, right next to the bus station. I was the only person on the tour. It was done by a former school principal. If you Google something like "day tours from Kirkwall," you'll get lots of results to consider.
You will not be able to spend any nights on Staffa. It is an uninhabited island. Fingal's Cave is there. Your best bet will be to take a tour of some kind.
A Hairy Coo day tour out of Edinburgh could hit some of the places on your list all in one day. There are several listed on the page I linked. I did one in May, 2016 and had a blast.
On that tour, I learned that the best time for heather is August. This link to Scottish Heather is about that.
Weather is always iffy in Scotland. May was cold and wet with sideways rain on the day of my tour on Orkney. Fortunately, I was well-prepared for it, but if I went to Scotland again, I'd go in late August when the heather is blooming.