You're close. The Norse settled mostly on the west coast, with the Thule culture mostly way up in the north, having spread there from the Canadian Archipelago. So not only was there a lot of ice, but also most of Greenland, between them. That being said, there were accounts of them meeting, but it wasn't a massive cultural exchange, suggesting that whatever trade or contact existed was relatively limited.
Where I'm from (Canada), that term is a slur, and although there are some individuals and groups who prefer to go by that term, best practice is usually to use a term that's not viewed by many as a slur. Yeah, some people prefer it, but also many find it outright offensive. In Canada, that tends to be First Nations, which in my experience hasn't ever been viewed negatively, but that might just be a cultural difference between here and the US.
It's important to remember that the indigenous peoples of the Americas are not a monolithic culture, society, or community, and that using a singular term as a catch-all for them isn't even really appropriate outside of specific contexts.