By horse
In colonial times people would usually walk to work and to other places they needed to be on a regular basis. Over long distances they would travel on horseback or on a donkey or mule, or by horse-drawn transport.
work
yes
yes
If it was across the sea, people traveled on boats to the new land. If it was in the same continent, they would travel by foot or in handcarts.
Wealthy plantation owners.
because no one cares haha
Farming
Some people have to because they work for a business that requires them to travel. Or some people travel for a vacation or to learn.
That answer is going to be different for different people. Some people don't work at all. For me, the answer is that I work from an office almost always, but I travel occasionally.
Colonial people had jobs such as schoolmaster, black smith, dressmaker, ect. Life was very hard work in colonial times.
People travel from curiosity - to see new places and experience new things. People also travel for business purposes or other work-related tasks.