I'm not sure of the context of this writing - if it is an article you are reading, or something you are writing yourself, but here are my interpretations:
1. It depends on the surrounding text. It most likely means 100 years before whatever event was just being talked about. If they meant 100 years before today, they would probably say "100 years ago".
2. Here, "at last" means "finally". So, it means, "Finally, in the early 17th Century, ..." and goes on from there.
3. It doesn't mean that everything was possible, but that everything seemed possible. The implied meaning is that the people had hope and were optimistic that with hard work and faith, it was possible.
4. It means in America there was a lot of religious excitement that inspired the people to write about Christianity. However, in Latin America (whichever countries these sentences are talking about), the people weren't as "excited" or "passionate" as Americans were, and thus didn't write as much about their religion.
5. You need the word 'but' here. It means that this man wanted to be a guide but the people didn't want him to be a guide, even though they used his maps. This is a complex sentence, so it may look unnecessary to have "but, though" together, but they are both needed to convey the right meaning.