They can indeed. This site talks about different types of essays, all of which I have seen taught in schools.

These four types are expository, persuasive, analytical, or argumentative.

The latter two are of the type commonly considered to be typical of academic essays.

The analytical essay should, as the name suggests, present a formal analysis. One should:

Be “objective” [and] avoid using the first person too much

and one should not:

Use slang or colloquial language (the language of informal speech) [or] contractions.

An argumentative essay should

prove that your opinion, theory or hypothesis about an issue is correct [and] be a topic that you can support with solid evidence

(and, by extrapolation, use formal language as for an analytical essay).

An expository essay, however, is more about personal response:

Your reaction to a work of literature could be in the form of an expository essay, for example if you decide to simply explain your personal response to a work. The expository essay can also be used to give a personal response to a world event, political debate, football game, work of art and so on

and, in a persuasive essay:

You are presenting an opinion and trying to persuade readers

but in a less scientific way than in an argumentative essay.

Generally, there are still conventions that separate a personal essay from creative nonfiction; the latter might rely on narrative or characterizing devices, whereas the essay is likely to be more formal and use more straightforward, less "creative" devices.

Editorial opinion pieces in a newspaper can be classed as essays. Typically, they can use slang and first person, but don't tend to play with nonstandard syntax or narrative devices too much. Of course, there is a lot of leeway that depends on the newspaper's style and intended audience, among other things.

The American Scholar has a collection of essays that show how personal and nonacademic an essay can be.

As for whether an essay can be fictional:

I think the idea is that an essay will be based on truth, but can be subjective, while fiction would be called a story/creative writing or similar. I can't find a good source to back this up at present, though, other than the first link, which suggests that even the less formal essay types are about presenting your opinions/recounting your experiences, etc.

They can indeed be creative. This site talks about different types of essays, all of which I have seen taught in schools.

These four types are expository, persuasive, analytical, or argumentative.

The latter two are of the type commonly considered to be typical of academic essays.

The analytical essay should, as the name suggests, present a formal analysis. One should:

Be “objective” [and] avoid using the first person too much

and one should not:

Use slang or colloquial language (the language of informal speech) [or] contractions.

An argumentative essay should

prove that your opinion, theory or hypothesis about an issue is correct [and] be a topic that you can support with solid evidence

(and, by extrapolation, use formal language as for an analytical essay).

An expository essay, however, is more about personal response:

Your reaction to a work of literature could be in the form of an expository essay, for example if you decide to simply explain your personal response to a work. The expository essay can also be used to give a personal response to a world event, political debate, football game, work of art and so on

and, in a persuasive essay:

You are presenting an opinion and trying to persuade readers

but in a less scientific way than in an argumentative essay.

Generally, there are still conventions that separate a personal essay from creative nonfiction; the latter might rely on narrative or characterizing devices, whereas the essay is likely to be more formal and use more straightforward, less "creative" devices.

Editorial opinion pieces in a newspaper can be classed as essays. Typically, they can use slang and first person, but don't tend to play with nonstandard syntax or narrative devices too much. Of course, there is a lot of leeway that depends on the newspaper's style and intended audience, among other things.

The American Scholar has a collection of essays that show how personal and nonacademic an essay can be.

As for whether an essay can be fictional:

I think the idea is that an essay will be based on truth, but can be subjective, while fiction would be called a story/creative writing or similar. The first link certainly suggests that even the less formal essay types are about presenting your opinions/recounting your experiences, etc. There is nothing to say that you can't lie or pretend, but that could mean your "essay" is reclassified when you are found out.

They can indeed. This site talks about [different types of essays][1], all of which I have seen taught in schools.

These four types are expository, persuasive, analytical, or argumentative.

The latter two are of the type commonly considered to be typical of academic essays.

The analytical essay should, as the name suggests, present a formal analysis. One should:

Be “objective” [and] avoid using the first person too much

and one should not:

Use slang or colloquial language (the language of informal speech) [or] contractions.

An argumentative essay should

prove that your opinion, theory or hypothesis about an issue is correct [and] be a topic that you can support with solid evidence

(and, by extrapolation, use formal language as for an analytical essay).

An expository essay, however, is more about personal response:

Your reaction to a work of literature could be in the form of an expository essay, for example if you decide to simply explain your personal response to a work. The expository essay can also be used to give a personal response to a world event, political debate, football game, work of art and so on

and, in a persuasive essay:

You are presenting an opinion and trying to persuade readers

but in a less scientific way than in an argumentative essay.

Generally, there are still conventions that separate a personal essay from [creative nonfiction][2]; the latter might rely on narrative or characterizing devices, whereas the essay is likely to be more formal and use more straightforward, less "creative" devices.

Editorial opinion pieces in a newspaper can be classed as essays. Typically, they can use slang and first person, but don't tend to play with nonstandard syntax or narrative devices too much. Of course, there is a lot of leeway that depends on the newspaper's style and intended audience, among other things.

[The American Scholar][3] has a collection of essays that show how personal and nonacademic an essay can be.

As for whether an essay can be fictional:

I think the idea is that an essay will be based on truth, but can be subjective, while fiction would be called a story/creative writing or similar. I can't find a good source to back this up at present, though. [1]: http://access-socialstudies.cappelendamm.no/c319365/artikkel/vis.html?tid=382115 [2]: https://www.creativenonfiction.org/what-is-creative-nonfiction [3]: http://theamericanscholar.org/dept/essays/

They can indeed. This site talks about different types of essays, all of which I have seen taught in schools.

These four types are expository, persuasive, analytical, or argumentative.

The latter two are of the type commonly considered to be typical of academic essays.

The analytical essay should, as the name suggests, present a formal analysis. One should:

Be “objective” [and] avoid using the first person too much

and one should not:

Use slang or colloquial language (the language of informal speech) [or] contractions.

An argumentative essay should

prove that your opinion, theory or hypothesis about an issue is correct [and] be a topic that you can support with solid evidence

(and, by extrapolation, use formal language as for an analytical essay).

An expository essay, however, is more about personal response:

Your reaction to a work of literature could be in the form of an expository essay, for example if you decide to simply explain your personal response to a work. The expository essay can also be used to give a personal response to a world event, political debate, football game, work of art and so on

and, in a persuasive essay:

You are presenting an opinion and trying to persuade readers

but in a less scientific way than in an argumentative essay.

Generally, there are still conventions that separate a personal essay from creative nonfiction; the latter might rely on narrative or characterizing devices, whereas the essay is likely to be more formal and use more straightforward, less "creative" devices.

Editorial opinion pieces in a newspaper can be classed as essays. Typically, they can use slang and first person, but don't tend to play with nonstandard syntax or narrative devices too much. Of course, there is a lot of leeway that depends on the newspaper's style and intended audience, among other things.

The American Scholar has a collection of essays that show how personal and nonacademic an essay can be.

As for whether an essay can be fictional:

I think the idea is that an essay will be based on truth, but can be subjective, while fiction would be called a story/creative writing or similar. I can't find a good source to back this up at present, though, other than the first link, which suggests that even the less formal essay types are about presenting your opinions/recounting your experiences, etc.