I think to get a substantive answer you will need to narrow down exactly who/what/when/where you are asking about; because as you point out, it really depends.

Not all "Europeans" were the same; the British, French, Spanish, Portuguese, Dutch, etc, all came to the Americas with very different aims. And even those groups are not homogenous; within the "British" or "Spanish" or what have you, there are vastly different policies and approaches- which change and vary depending on time and place.

So the difficulty in answering the question is really that it is too general- the Americas are huge and there are a vast number of different groups and peoples that inhabited it and the colonizers themselves are various and varied- it is difficult to speak about "Europeans" and "First People" because the terms are so broad that they cannot encompass any tangible coherent representation of the history from 1492 to 2014.

• For your first question- it depends and changes over time and space.

• Again, number two depends. Some military victories came quickly- like the Spanish over the Aztec; some were slow and always tenuous like the Spanish in the Yucatan right next door.

• The third question is the easiest to narrow down and definitively say, Yes. From the outset of colonization- or contact- there were those who advocated for indigenous 'rights' or respect. Writers like Bartolome de las Casas; Montaigne, and later Enlightenment thinkers were often proponents for indigenous peoples- though even here, they vary wildly because as you indicate with your quotation marks, "rights" is an anachronism, so their advocacy and goals are of course varied. De las Casas is perhaps the easiest to understand and read- he was very clearly attacking Spanish abuse of indigenous laborers and arguing for the existence of a soul in the indigenous peoples.