This is going to widely vary depending on who you ask and I would say most people have probably never met a full-blooded Native American. Overall, I would say most people couldn't tell you the first thing about relations between whites and Natives because, well, everyone can just ignore it. The only real time I ever see it brought up in the news is when people debate the Washington Redskins name debacle.
I spent some time on a Navajo reservation recently, and it was certainly an eye-opening experience. It was different from anything I'd ever experienced. There are many different reservations and tribes, so I cannot speak for everyone — and I'm not trying to speak for Native Americans, just speaking on my experience with what I witnessed and was told to maybe answer part of your question.
Also, various tribes prefer various names, but the people I stayed with said that they preferred "Native American" and found it insulting if they were called anything else (like Indian, etc.) so I'm gonna go with that for the duration of this post.
The reservation I stayed at was miles away from a town; the nearest store was 40 minutes off the reservation and the prices were jacked up because the store has a monopoly on the town and reservation even though almost everyone on the reservation is dirt poor. The reservation is mostly, if not totally, governed by the Navajo Nation; they have their own government, from my understanding. However, they also receive federal funds and receive healthcare from the federal government (which is really shitty, from what I know). It's sorta confusing, and I don't know a lot about it so I can't really speak to that. "It's complicated," is probably the best answer to explain the relationship between tribal governments and the federal government.
Where I was at, most people interacted mainly with other Natives and there was a very small white population in the town; on the reservation, of course, the white population was nil. So I would say actual relations between Natives who live on a reservation and whites is very limited unless the reservation is near a town full of white people. There are definitely cultural differences and I think there's a lot of misinformation; some whites think that Natives get all this money from the government and then just throw it into casinos, when in reality, that's not true. It's a very complicated thing; there's certainly bad blood between whites and Natives, and you're going to have some of each who are distrustful of the other. The Native Americans I spoke with all basically said, "Look, there are some people on the reservation who don't like whites, but we treat everyone with respect and ask to be treated the same."
Living conditions on the reservation I was at were pretty bad; part of it is their culture. They're fine with simple conditions and because of their rich history and culture, they don't necessarily want all of the "luxuries" people off the reservation have, like fancy cars, TVs, etc. But at the same time, they're poor and can't afford a lot, either. They got electricity 10 years ago and don't have running water. Their houses are all small. But I think it's a mix between not wanting a lot and also being stuck with shitty conditions because of the hand they've been dealt. The biggest thing I noticed (aside from the lack of running water) was how they disciplined their kids; very different from the typical helicopter parent stereotype. If they told the kids to get out of the house and go play outside, they went and played outside, no questions asked. The kids also have a huge amount of responsibility — kids as young as 8 know how to cook, get water from the well, etc.
They told me there's a huge drinking problem on the reservation. It's illegal to drink on the reservationI was at, but it's a desolate place, so a lot of people turn to the bottle. Because it's popular but illegal, a six-pack of beer can go for upwards of $60.
The roads on the reservation were pretty bad; they get washed out every time there's a heavy storm and then the buses can't get through, so the schools get shut down a lot for rain or snow that normally wouldn't get places shut down.
Those are the basics. I only spent a week with them, and I'm sure I'm still very ignorant to many things, but it was a very eye-opening experience and I learned a lot. But again, I can only speak to what I witnessed and heard at the place I was at; there are so many tribes and reservations that are all different and what one reservation does (or even what one family on the reservation does) doesn't go for all the rest, so keep that in mind.