I'll be a little less pessimistic of your plans. Keep in mind that many of us here are older and while many still travel on budget, there is a big difference between budget travel and the college-roaming-Europe travel. I did many of the things your are considering once (many years ago) and in some ways it is easier to get around now and in some ways not as easy.
First, do consider how much you are traveling from point to point. There is an expense in doing that and while some places can be quickly seen in a couple of days, you will absorb more if you slow it down just a bit. Or don't have such a wide net of the continent to cover. Two months seems like a lot, but the time will go quickly. You might also find yourself burned out after a month so be prepared to have a day or two every so often to just rest.
Do some cost comparisons on a Eurail pass verses advanced ticket discounts. You are still young enough to get 2nd class so it will make it cheaper, but often it is much cheaper to buy in advance. But if you don't know the exact schedule and want to be flexible, a pass might still work for you. Keep in mind that all high-speed trains and some others now require seat reservations in addition to the pass (and that comes with a cost).
You have a situation in which you have more time than money. I've done a fair amount of that type of travel and so I don't think it's so bad to take busses and trains. You see a lot of great landscape and countryside that way. Especially considering your sinuses, don't worry about not taking flights.
The most expensive places to visit on your list are London, Paris, and Barcelona. Copenhagen isn't cheap, but skipping alcohol is a good way to avoid excess costs there. The city also has good street food so you can avoid more expensive meals. I've done well on the cheap with street food, buying some essential groceries that I carry along with me and ethnic food in places like London and Paris. Never a need for fast food either.
I've never slept outside myself but it seems many places have cracked down on such things. Carefully understand the rules and laws and always be aware of your own security.