Στη λεωφόρο έχει πάντα κίνηση το απόγευμα, γι’ αυτό προτιμώ να παίρνω το μετρό.

Στη is a contraction of σε + τη(ν):

• σε = in / on / at / to (very flexible in Greek)
• τη(ν) = the (feminine singular accusative) So Στη λεωφόρο literally means on the avenue / on the boulevard. In everyday Greek this contraction is extremely common: στο (σε + το), στη (σε + τη), στους (σε + τους), etc.

Two reasons: 1) Greek needs the noun with its article in most normal statements: τη λεωφόρο = the avenue.
2) After the preposition σε, the noun phrase is typically in the accusative. So you get σε + την λεωφόρο → στη λεωφόρο.

In Greek, έχει (literally it has) is commonly used like there is / there are, especially with things like traffic, noise, people, etc.

• Έχει κίνηση = There is traffic / It’s busy (traffic-wise)
  So Στη λεωφόρο έχει πάντα κίνηση = On the avenue there’s always traffic.

Without an article, κίνηση is more general: traffic (as a phenomenon) rather than a specific, known “the traffic”.

• Έχει κίνηση = There’s traffic / It’s busy
• Έχει την κίνηση would sound like a specific, identifiable traffic situation (less natural here).

πάντα = always. Here it modifies έχει … κίνηση (the fact that there is traffic).
Greek word order is flexible, but placement changes emphasis:

• Στη λεωφόρο έχει πάντα κίνηση (neutral)
• Πάντα έχει κίνηση στη λεωφόρο (emphasis on always)
• Στη λεωφόρο πάντα έχει κίνηση (also fine)

Greek often uses the article with time expressions, especially when you mean in the afternoon / during the afternoon (as a general time period):

• το πρωί = in the morning
• το βράδυ = in the evening/at night
• το απόγευμα = in the afternoon
  You can also hear απόγευμα without the article in some contexts, but το απόγευμα is very standard here.

γι’ αυτό means that’s why / for this reason.
It comes from για αυτό, but Greek often drops the final vowel of a word before another vowel (elision), and marks it with an apostrophe:

• για αυτό → γι’ αυτό

να introduces the subjunctive in Modern Greek. After many verbs (including προτιμώ = I prefer), Greek uses να + verb where English often uses to + verb:

• προτιμώ να παίρνω = I prefer to take (literally: I prefer that I take)

να + present often expresses a habitual / general preference:

• προτιμώ να παίρνω το μετρό = I prefer to take the metro (generally / as a habit)
  If you were talking about one specific occasion, you might hear a different aspect depending on meaning (e.g., a more “one-time” feel), but for a routine choice, the present is natural.

Yes. παίρνω is very common for using transport:

• παίρνω το μετρό = take the metro
• παίρνω το λεωφορείο = take the bus
• παίρνω ταξί = take a taxi

Yes, μετρό is neuter in Greek, so it takes το in the singular:

• το μετρό (neuter singular) In this sentence it’s the direct object of παίρνω, so it’s in the accusative—but for neuter singular, nominative and accusative look the same (το μετρό).

Yes, but it would sound a bit more formal/neutral depending on context:

• Στη λεωφόρο υπάρχει πάντα κίνηση το απόγευμα = also correct
  In everyday speech, έχει κίνηση is extremely common and often sounds more natural.