The Town I Live Iin Aand Tthe City I Commute To ¶
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I live in a small town but have to commute to another city for work.

Short prepositions like "in", short conjunctions like "and" and articles like "the" are generally not capitalised in titles. However, an exception to this is that the first and last words of a title are always capitalised. You can see it here: although "to" is considered a short preposition, it's still capitalised because it is the last word in the title.

There are affluent districts with spotless streets in the east of [the] town while in the west (of it) you can see many run-down, abandoned houses.

(1) Both "the east of town" and "the east of the town" are perfectly acceptable. However, there is an extremely subtle difference in tone between them. The former would imply some degree of familiarity, closeness, or association with the town. Since you live in the town, "the east of town" is valid and natural. Conversely, the latter would convey a feeling of dissociation or objectiveness, as if you are an external observer with no ties to the town. It is also perfectly valid and natural here, if you are going for a more factual and objective description of the town.
(2) You might consider omitting "of it", since the reader will understand that you're referring to the west of the town.

As a result, many people from the western part are leaving the town, as they don't want their children to be deprived of [the] many opportunities they could potentially enjoy.

(1) Similarly to saying "the east of town", you can also say "many people...are leaving town" here. Of course, both are valid.
(2) In my view, using "the" would be more natural. This is somehow related to your use of "many": if you hadn't used it, both "be deprived of opportunities" and "be deprived of the opportunities" would sound equally reasonable to me. However, I apologise that I'm unable to provide a satisfactory explanation for this.

There are also environmental problems here: the two local ponds are polluted because of [an/the - ?

Both "an" and "the" are equally acceptable here; it simply depends on the degree of specificity you want to convey and the importance you want to give to the factory. Neither completely rules out or absolutely implies the existence of other factories.

Here, I suggest the use of "an" over "the", since this is the first time you're introducing the factory to the reader, who is likely not part of the town. Nonetheless, "the" can still be used in first introductions, and you might see this being applied in fiction. For example, when a novel starts with the sentence "He stood before the castle gates.", it immediately establishes the importance of said castle. Additionally, it is also commonly used to accompany further information which specifies the factory you're referring to, such as in the phrase "the old factory NEARBY (as opposed to any other factory)".

Up-and-coming artists and actors are moving to the cityhere, and when leaving the city in any direction, you can see sprawling suburbs.

I'd suggest replacing "to the city" with "there", to avoid excessive repetition of "city".

Although I live fromin the east of the town, I'm considering moving to the city as in the future.

The Town I Live In And The City I Commute To ¶
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I live in a small town, but have to commute to another city for work.

There are affluent districts with spotless streets ion the east of [the]side of town meanwhile ion the west of itside you can see many run-down, abandoned houses.

I don't think the town is well-run in this regard - the authorities do almost nothing to balance the standards of the two areas.

There are also environmental problems here: the two local ponds are polluted because of [an/the - ?

I would personally use "an" because the listener can ask for further elaboration on whether if it's the only factory. Using "the" would imply that somehow the listener already knows of the factory's existence.

There supposedly is only one] old factory.

The life there is vibrant and sometimes chaohectic.

"Hectic" has a much softer connotation than "chaotic". Hectic means that it's busy and bustling but not too overwhelming. "Chaotic" for me evokes a more disorderly image.

Although I live from the east of the town, I'm considering moving to the city as well in the future.

I want to become a singer and I'm currently, I'm preparing for an audition.

Cities [01A-2]

I don´t know what 01A-2 means. Is it necessary to put in the title?

The Town I Live Iin Aand Tthe City I Commute To ¶
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I live in a small town but have to commute to another city for work.

Title case has weird capitalization rules, but the title should look like that.

You could also say:

I live in a small town, but I have to commute to another city for work.

There are affluent districts with spotless streets ion the east of [the] townside where the city is, while ion the west of itside you can see many run-down, abandoned houses.

I usually say and hear of "sides" or "parts" when talking about divisions within a town. I added "where the city is" to make it clearer later on that when you say "the city" you mean "the eastern part."

I don't think the town is well-run in this regard - --the authorities do almost nothing to balance the standards of the two areas.

To indicate a pause, a double dash (em dash) is used without spaces.

As a result, many people from the western part are leaving the town, as they don't want their children to be deprived of [the] many opportunities they could potentially enjoy elsewhere.

For naturalness, I think "elsewhere" or "somewhere else" is better. Also, maybe consider omitting "potentially," since it is already implied by the word "could." Or "would potentially" could, or would potentially, be another option.

There are also environmental problems here: the two local ponds are polluted because of [an/the - ? old factory.

"an" might be preferable here, but "the" would be acceptable. However, "the old ____ factory" would be pretty normal (where the type of factory goes in the blank space).

There supposedly is only one] old factory.

Up-and-coming artists and actors are moving to the cityhere, and when leaving the city in any direction, you can see sprawling suburbs.

Maybe consider for greater conciseness:

Up-and-coming artists and actors are moving there, and you can see sprawling suburbs in every direction.

Also, "city" doesn't have to be repeated this way.

Although I live fromin the east side of the town, I'm considering moving to the city as in the future.

If you live there, it would be "live in."

Another option is "Although I come from the east side of town..."

I want to become a singer, and I'm currently, I'm preparing for an audition.

The Ttown I Llive Iin Aand Tthe Ccity I Ccommute To ¶
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I live in a small town but I have to commute to another city for work.

There supposedly is only one] old factory.