Hi, It is an idiom to express when people do something in a way that is the opposite or contrary to what is generally considered normal, logical, accepted. We have other similar expressions like swimming or going against the current.. Again, the idea is you choose the hard way to do something. Below is link to a dictionary of idioms that may help you. https://idioms.thefreedictionary.com/go+against+the+grain

Your examples don't sound natural. Usually, the phrase is a fixed phrase "He/she goes against the grain." "go against the grain" refers to woodworking with a plane. Removing a small amount of wood with a plane is easy "with the grain" (in the direction of the wood grain). It is hard "against the grain" (in the opposite direction of the grain). By analogy, "go against the grain" can mean "to go against" the traditional approach (leading to opposition). Also, it can have the general meaning of "to upset people" (like stroking a cat's fur the wrong way) and "to do things the hard way."

Yes, it definitely means to neglect your habits and act completely unexpected.

Unsuitable or unacceptable.

You should not use 'the' with 'society'. It is one of those nebulous exceptions (like 'space') that do not take an article.