I hope you're aware that almost half (~45%) of all Europeans actively support further integration towards a federation of nation-states, which you can check
here (page 154). Mind you, the number that don't know go from 10-30% from country to country. I.e., if there was a referendum for that back then, EU would be a federation right now. You should also keep in mind that this was 2014, when people had worse views of the EU. In fact, that was the all-time low for the EU image. You can cross-check with Eurobarometer from 2017, if you don't believe that. Another thing to note - if you disregard the UK in the result for how many support a federation (in the UK, it was 21%), then you'd get that about 50% of Europeans supported it. Imagine what that number is right now.
Not that I actually think the EU should become a federation now. At least 20 more years, in my opinion.
- - - Updated - - -
I don't know exactly because I'm not a politician, but I do know the current state of things isn't as it should be. And no, I don't think either of those two things should be done. I definitely do not support any sort of forced austerity, because that is not how a country gets out of a crisis. It gets out by reducing its taxes and attracting investments again. So this would probably be a good start - some sort of mechanism to stimulate investments in countries that are going through a crisis. This would involve "giving free money" to these countries, but in a very targeted way, similar to how EU research funds are given out.
Yes. States must be equal, as bizarre as this may seem given their populations. The reason is very simple - having a say that is disproportionate to their size is almost the only reason why small entities are part of larger ones. The bigger countries get more control of the market, while smaller countries are somewhat compensated by more control of the political arena.
What will happen is what always happens in democratic regions of the world - the losers (disagreers) suck it up. They will whine, but they wont start civil wars. And I very much support refugees being distributed more rationally, even if it's forced. I'm completely dumbfounded that they weren't distributed uniformly.