We don't have the space to address every element of your question, but let me get you pointed in the right direction. These three advancements were part of a time period now referred to as the Transportation Revolution. Individually and together, they made it easier for Americans to migrate, to settle the West, to trade with other states and to communicate over distance.
Immigration was already taking place due to the vast reaches of farmland available for settlement, but the Transportation Revolution accelerated it, and made farming and doing business on the Mississippi frontier of that time more possible.
The steam engine was key for steam powered ships, and allowed us to safely and easily navigate both upriver and downriver and across the seas without wind power. The economy expanded as a result, as did the western population and agricultural output.
National unity was also affected, as the TR was something like an early form of internet, tying the various parts of the country more closely together economically and socially.