1. The British and the French were both growing powers in Western Europe. Traditionally the two were not in the best of relations, and there were constant tensions between them, often resulting in military conflicts as well.
There were numerous reasons as two why the two empires disliked each other, especially during the colonial era.
A major reason was the competition for gaining new territory, be it in the new world, or in the old world. Both empires had big aspirations and wanted to control as much territory as possible. This led to them standing on each other's way, so the conflicts were somewhat inevitable.
Both empires wanted to gain access to as many resources as possible in order to gain more wealth, and again they were standing on each other's way all the time.
Another reason was also the religion, as the British became more liberal and largely distanced themselves from the Pope, while the French were in close ties with the Pope.
2. The transcontinental railroad was revolutionary for the development of the United States. This construction enabled quick movement of people and goods over large territories. The East Coast and the West Coast became directly connected, and in between them was the interior of the country which became connected with both.
This made the migration of the people much more ease. Because the goods were transported quickly and easily, the people started to produce more, which resulted in economic boost. Since the economy was thriving, and the transportation and movement became easy and quick, lot of new cities were established in the western part of the country.
3. The population density in North America is not the same or similar everywhere. The continent tends to often be divided by the 100th meridian, or rather east and west of it when it comes to the population density.
The reason for this division is the big difference of the population density east and west of this imaginary line.
East of the 100th meridian, the population density is high. There are much more cities, towns, agglomerations, all which are very close to each other and have large populations. West of this line the settlements are much more sparsely distributed, and they also tend to have lower populations.
There are two basic reasons for this disproportion. One reason is that the East Coast was settled first, so all along the coast there were lot of cities that were established and later well developed and prosperous, while in meantime the west was still unknown. Another reason are the geographic factors. The East tends to have better climate, the topography in general is suitable for settlements, and the landscape is naturally covered with dense vegetation. The West on the other hand, has much more mountains, which are also very high. There are deserts, as well as several semi-arid areas. In lot of places there is lack of natural resources, especially water, and the climate tends to be more extreme.
4. When the United States managed to gain control west of its initial colonies on the eastern coast, the government immediately tried to motivate the people to start migrating toward the west. The goal of the government was simple, to move as much people as possible westwards so that it can gradually form strongholds, have dominant population, and use the natural resources of the area.
The US government tried to achieve its goal with the creation of Manifest Destiny. Manifest Destiny was an act through which the people that wanted to move toward the western lands were getting large portions of land for either were small fees, or even for free in some cases. The only condition was that the people that apply for land have to develop it agriculturally, make a permanent dwelling, and live there for at least five years.
This was seen as a huge opportunity by lot of people, so there was an abundance of people moving in, especially the new immigrants. This resulted in rapid development of the west, and it quickly became one of the largest agricultural regions in the world. Also, the region experienced rapid demographic boom, as well as economic progress.