Es posible que el tren llegue con retraso, así que salgo temprano.

Because es posible que expresses uncertainty/possibility, and that kind of clause normally triggers the subjunctive in Spanish. So you use llegue (present subjunctive) rather than llega (present indicative).

A practical rule: expressions that communicate doubt, possibility, uncertainty, or subjective evaluation often take que + subjunctive.
Es posible que + [subjunctive] is a very common fixed pattern.

Llegue is present subjunctive, third person singular (yo llegue, tú llegues, él/ella/usted llegue…). It does not mean present time by itself; it often refers to a future possibility after triggers like es posible que.

It’s a spelling change to keep pronunciation consistent. The verb is llegar. Before e/i, g would sound like the English H (as in gente). To keep the hard g sound (as in gato), Spanish writes gu: llegue, llegues, lleguen.

Yes. Puede que + subjunctive is very natural in Spain and means essentially the same: It may be that…
Your sentence and Puede que… both commonly use the subjunctive.

Con retraso means delayed / late (literally, with delay). Other natural options include:

• que el tren llegue tarde (arrive late)
• que el tren venga con retraso (if you’re focusing on it coming toward you)

Spanish often uses the present to talk about scheduled or intended near-future actions, especially when it feels planned: así que salgo temprano = so I’m leaving early / so I leave early (today).
You could also say saldré temprano to sound more explicitly future.

• Salgo temprano: sounds like a plan/arrangement, often immediate or already decided; very conversational.
• Saldré temprano: more clearly future, sometimes more formal or deliberate.

Both are correct here.

Así que means so / therefore (introducing a consequence). It often feels like a direct logical result.
Entonces can also mean so/then, but it’s slightly more general and can sound more like in that case or then in a sequence.

Yes. Así meaning in this way / thus is written with an accent: así. Without the accent (asi) is generally not correct in standard Spanish.

Because the sentence is combining two independent ideas:
1) Es posible que… (possible situation)
2) así que… (result/action you take)
The comma helps separate the cause/condition from the consequence. It’s very common punctuation with así que.