Learn Hardcore Japanese: hayame ni okireba, eki made aruite ikemasu. - If I wake up early, I can walk to the station.

早め is a na-adjective (or noun) meaning “a bit early” or “earlier than planned.” Adding に turns it into an adverb that modifies a verb. So 早めに起きる literally means “get up a little early,” i.e. “get up earlier than usual.”

What grammar point is 起きれば?

This is the conditional ば-form of 起きる. In Japanese, the ば-form expresses “if” or “when” in a general sense. Therefore 早めに起きれば means “if you get up early.”

What does 駅まで indicate?

まで marks the endpoint of movement or a range. 駅まで means “up to the station,” so it tells us that the walking goes as far as the station.

Why is it 歩いて行けます instead of just 歩いて行きます or 歩けます?

Here we have the て-form of 歩く plus the potential form of 行く.

歩いて行きます = “go by walking” (just states how you go)
歩いて行けます = “can go by walking” (expresses ability)
歩けます = “can walk” (no destination specified)
Since the sentence wants to say “you’ll be able to walk to the station,” 歩いて行けます is the correct choice.

Could I say 早く起きれば instead of 早めに起きれば? What’s the difference?

早く simply means “early,” whereas 早めに carries the nuance “a little earlier” or “ahead of schedule.” In many contexts they’re interchangeable, but 早めに起きれば suggests getting up slightly earlier than you normally do or than planned.

Why is the subject missing in this sentence? Who is doing these actions?

Japanese frequently omits subjects when they can be inferred from context. In this case the implied subject is “you,” giving advice or stating a possibility: “If you get up early, (you) can walk to the station.”

What nuance does the ば conditional bring here? Could I use たら or と instead?

The ば conditional expresses a general, often more formal, condition and its likely result.
たら is more conversational and can refer to a specific occasion.
と implies an automatic or inevitable result and isn’t normally used for advice.
You could say 早めに起きたら駅まで歩いて行けます, but 早めに起きれば sounds more general and slightly more formal.