Here are the answers to the questions based on the provided text:

1. **Which city is the most densely populated in the US?**
- New York City is the most densely populated city in the US.

2. **Which field does New York exert a significant impact upon?**
- New York exerts a significant impact on finance, media, entertainment, art, fashion, research, technology, education, and sports.

3. **Who colonised the trading post in Lower Manhattan?**
- The trading post in Lower Manhattan was colonised by the Dutch Republic and was later taken over by the English.

4. **When did New York serve as the capital of the US?**
- New York served as the capital of the US from 1785 until 1790.

5. **Which symbolizes the US and its democracy?**
- The Statue of Liberty symbolizes the US and its democracy.