I never said that immigrants explointing the welfare system don't exist, but at least in Austria it's a fact that immigrants on the whole pay more into the system than they receive. And the whole argument is often nothing more than cynical with this recent wave of immigrants, who are legitimitely fleeing war.
With the requests, they're often delibirately delayed as to not allow the families of the asylum seekers to join them. That and problems concerning the Dublin convention (stating that every immigrant is the responsility of the land they first stepped foot on in the EU, which basically leaves it all to Italy, Spain & Greece), which as a whole is incredibly flawed and should be changed as soon as possible imo.
Oh come on, now you're not even trying anymore.
Not sure what exactly you're referring to with unregulating health care, but in general public healthcare simply is the only system that has consistently worked very effectively in dozens of cases, while I don't know of a single instance in human history where private insurance schemes have actually been able to provide coverage for an entire society. Of course it never having been succesful in the past in no way means that it won't ever be able to work in the future, but it's a pretty solid indicator imo, especially considering that I'm also yet to hear of a viable theoretical model involving private health insurance that doesn't include a sizeable portion of society being left uncovered.
Concerning education, I see what you're trying to get at, but that's not primarily an issue of private vs. public (tertiary) education, but mostly about whether a lot of the college courses nowadays actually make sense. And while there's some truth to that in my opinion as well, it's still a fact that pretty much every job position of higher quality requires college degrees, so private universities & tuition fees simply add a lot to hereditary poverty & inequality, and leads to a shitton of wasted potential.