What are the implications of “Self-Reliance” for religion, government, traveling, art, and property ownership?

The implications of "Self-Reliance" stem from Ralph Waldo Emerson's belief that people are responsible for their own lives and should spend time developing themselves, accepting control of their lives, and forging their own path rather than following the paths of others.
"Self-Reliance" rejects the idea of institutionalized religion. Emerson believes that religion—like marriages, arts, and occupations—were chosen by society. It's as if people have been funneled into those things rather than confidently choosing them as a reflection of their own beliefs and desires. He believes that nothing—including religion—brings peace but one's own self. However, that doesn't mean he thinks religion is inherently bad. He just thinks that it can stifle self-reliance and encourage a dangerous group mentality that doesn't make a person figure out their own answers.
Emerson is very clear that people control the government because the citizens of the country are the ones who give the government power and operate the government. He also thinks that one shouldn't be reliant on the government. He thinks that people put the government in the position of protector of what they care for and fail to realize that the government only has the power that individuals give to it.
For Emerson, travel for the purpose of travel is unnecessary. He says that "the soul is no traveller; the wise man stays at home, and when his necessities, his duties, on any occasion call him from his house, or into foreign lands, he is at home still." He goes on to say that you should travel with the personality and mindset of a king rather than an interloper or valet. He says that traveling without purpose—just looking for amusement—leads to one growing old and away from his own self. Emerson says that travel is a "fool's paradise."
One point that Emerson makes about art is that it's not necessary to emulate the works of past masters. He says:

And why need we copy the Doric or the Gothic model? Beauty, convenience, grandeur of thought, and quaint expression are as near to us as to any, and if the American artist will study with hope and love the precise thing to be done by him, considering the climate, the soil, the length of the day, the wants of the people, the habit and form of the government, he will create a house in which all these will find themselves fitted, and taste and sentiment will be satisfied also.

This is a call for people to create their own art and to find the confidence to do so. He seems to say that people should do what feels right to them instead of doing what they've been trained to do by society. He says it's important to "insist on yourself" and "never imitate." Because he believes that every man is unique, he believes that you cannot be instructed to greatness but rather must find it yourself.
For Emerson, the important thing about property ownership is not to become reliant on the property. A man should be reliant on himself—not on what he owns and what people can take away from him. Property can also be taken away by natural disasters or acts of God. People should shy away from any pride in their property. If they got it without effort, they should be ashamed of it. Property can also weaken you rather than help strengthen you if you begin to rely on it.
The essential thing to take from "Self-Reliance" is that Emerson believes people should create their own destinies and ways of living. He believes in their personal power. Emerson doesn't explain to people how to live their lives; rather, he tells them to decide how to live their lives and to be true to themselves. That is what creates a variety of implications for things like religion, government, art, travel, and property ownership.