To recap, here are your questions again:
What's the tax rate for countries offering "universal healthcare?"
There are a ton of countries that do this. The tax rate varies. There are income taxes, VAT taxes and many other taxes. If you provided yourself more info, like "What are the income tax rates for countries X, Y and Z?", then that's easily findable.
What's the wait time for appts?
Again, this is too broad. What kind of appointments? Urgent care? Specialists? General practice? Checkups? If you answered those questions (along with which countries) for yourself, then sure, you could find the answers relatively easily.
What's the cure rate for major diseases?
Which diseases? A lot of "major diseases" don't have cures, just treatments. So, what outcomes specifically are you looking for?
What countries do you need additional health coverage (out of pocket) in?
You'd have to specify what you mean by "need". The point of universal healthcare is that you don't "need" anything else. In some countries, you can get private insurance, and that might help in certain ways.
So, yes, there are a lot of graphs out there on the general topic of universal healthcare systems. To find ones (or info) for your questions, you'd need to provide more info.
