Я дойду до метро пешком, а потом поеду домой.

Дойду is the 1st person singular future of дойти, a perfective verb meaning to get to / to reach on foot.

So Я дойду до метро means I’ll walk as far as the metro / I’ll reach the metro on foot.

By contrast:

• иду = I am going / walking right now

• дойду = I will get there on foot

  Russian often uses a perfective verb here because the speaker is talking about a completed result: reaching the metro.

These are related, but they focus on different things:

• пойду = I’ll go / I’ll set off on foot
  Focus: starting the movement

• дойду = I’ll get there / I’ll reach it on foot
  Focus: reaching a point

• приду = I’ll arrive
  Focus: arrival at a destination, often without emphasizing the path

In Я дойду до метро пешком, дойду is especially natural because the sentence means the speaker will walk up to the metro and then continue in another way.

Yes. Both are simple future forms.

That is because дойти and поехать are perfective verbs. In Russian, perfective verbs do not have a true present tense. Their present-looking forms actually refer to the future:

• дойду = I will reach
• поеду = I will go by transport

Compare with imperfective verbs:

• иду = I am walking
• еду = I am going by transport

So in this sentence, both actions are future and sequential.

The preposition до means up to, as far as, or until reaching. It is used with the genitive case.

So:

• до метро = up to the metro / as far as the metro

This fits the idea of walking to a certain point and then changing how you travel.

Because метро is an indeclinable noun in Russian. That means it usually keeps the same form in all cases.

So although до requires the genitive, метро still stays метро:

• метро
• до метро
• к метро
• в метро

The case is shown by the preposition and the sentence structure, not by a change in the noun itself.

Пешком means on foot. Historically and grammatically, it is an instrumental-form adverbial expression.

In modern Russian, learners usually just memorize it as the standard way to say on foot:

• идти пешком = to go on foot
• дойти пешком = to get there on foot

There is no preposition here. You simply say пешком.

Because after reaching the metro, the speaker will continue by transport, not on foot.

Russian distinguishes between:

• идти / пойти = go on foot
• ехать / поехать = go by vehicle/transport

So:

• дойду до метро пешком = I’ll walk to the metro
• потом поеду домой = then I’ll go home by transport

Using поеду strongly suggests travel by metro, bus, car, etc.

Домой is a very common adverb meaning homeward / to home.

Compare:

• домой = home, in the sense of movement toward home
• дома = at home
• в дом = into a house/building
• к дому = toward the house/building

So поеду домой means I’ll go home.

This is the normal word Russians use when talking about going home.

А often connects two clauses when there is a slight contrast, transition, or change of stage.

Here the sentence has a natural two-part structure:

• first, walk to the metro
• then, go home by transport

So а потом sounds like and then / and after that, with a mild sense of switching to the next step.

И потом is possible in some contexts, but а потом sounds very natural here because the mode of movement changes.

Because а is a coordinating conjunction joining two clauses:

• Я дойду до метро пешком
• а потом поеду домой

In Russian, when two clauses are joined by а, a comma is normally required.

So the comma is standard punctuation here.

Yes. Russian word order is flexible, and different orders can sound more natural depending on emphasis.

For example:

• Я дойду до метро пешком, а потом поеду домой.
  Neutral, very natural

• Я пешком дойду до метро, а потом поеду домой.
  Slightly more emphasis on on foot

• До метро я дойду пешком, а потом поеду домой.
  Emphasis on to the metro

Also, я could be omitted if the subject is already clear:

• Дойду до метро пешком, а потом поеду домой.

The original sentence is a normal, neutral way to say it.