Τον Οκτώβριο φοράω μακρυμάνικα ρούχα και πίνω πιο πολύ ζεστό τσάι.

Because Greek often uses the accusative for time expressions meaning in / during a month, season, or day.

• ο Οκτώβριος = October as the dictionary form
• τον Οκτώβριο = in October

So this is a very common pattern:

• τον Νοέμβριο = in November
• την Τρίτη = on Tuesday
• το καλοκαίρι = in the summer

The article τον is part of that pattern.

Greek often leaves out subject pronouns when they are already clear from the verb ending. This is called a pro-drop language.

Here:

• φοράω = I wear
• πίνω = I drink

The endings already tell you the subject is I, so εγώ is unnecessary.

If you add εγώ, it usually gives emphasis or contrast:

• Εγώ φοράω μακρυμάνικα ρούχα = I wear long-sleeved clothes

Not necessarily. In this sentence, the present tense describes a habit or usual action.

So φοράω and πίνω here mean something like:

• I usually wear
• I tend to drink

Because of τον Οκτώβριο, the meaning is habitual: what the speaker does in October in general, not only at this exact moment.

Yes. They are two forms of the same verb, and both mean I wear.

• φορώ is the shorter form
• φοράω is very common in everyday speech

A learner will often see both. In modern spoken Greek, φοράω is extremely natural.

Also remember that φοράω / φορώ can mean either:

• I wear
• I put on

depending on context.

Because μακρυμάνικα is an adjective agreeing with ρούχα.

The noun ρούχα means clothes and is neuter plural, so the adjective also has to be neuter plural:

• μακρυμάνικος = masculine singular
• μακρυμάνικη = feminine singular
• μακρυμάνικο = neuter singular
• μακρυμάνικα = neuter plural

So:

• μακρυμάνικα ρούχα = long-sleeved clothes

Greek normally uses ρούχα in the plural for everyday speech, where English might use either clothes or clothing.

So μακρυμάνικα ρούχα is the natural everyday Greek way to say this idea.

A learner should not expect Greek to match English exactly here:

• English: clothing can be singular and uncountable
• Greek: ρούχα is usually plural

Because τσάι is a neuter singular noun: το τσάι.

Greek adjectives must agree with the noun in gender, number, and case. So the adjective must also be neuter singular:

• ζεστός = masculine
• ζεστή = feminine
• ζεστό = neuter

Therefore:

• ζεστό τσάι = hot tea

Here πιο πολύ means more.

So:

• πίνω πιο πολύ ζεστό τσάι = I drink more hot tea

It compares the amount of tea the speaker drinks in October with some other time.

A very common alternative is περισσότερο:

• πίνω περισσότερο ζεστό τσάι

That means essentially the same thing.

This is an important difference.

• πιο πολύ ζεστό τσάι = more hot tea
  The amount is greater.

• πιο ζεστό τσάι = hotter tea
  The temperature is higher.

So in your sentence, πιο πολύ goes with the idea of quantity, not temperature.

Yes, often it can.

Greek can leave out the noun when it is obvious from context. So both of these are natural:

• φοράω μακρυμάνικα ρούχα
• φοράω μακρυμάνικα

The second one literally means something like I wear long-sleeved ones, but in natural English we would usually still translate it as I wear long-sleeved clothes or I wear long sleeves.

Yes. Greek word order is more flexible than English word order.

This sentence is natural:

• Τον Οκτώβριο φοράω μακρυμάνικα ρούχα και πίνω πιο πολύ ζεστό τσάι.

But you could also say:

• Τον Οκτώβριο πίνω πιο πολύ ζεστό τσάι και φοράω μακρυμάνικα ρούχα.

The basic meaning stays the same. Changing the order usually changes focus or emphasis, not the core meaning.

Still, πιο πολύ should stay close to the part it modifies, so the sentence remains clear.