Ми підемо туди пішки.

Підемо is the 1st person plural future form of піти.

So:

• піти = to go / to set off once, in one direction
• підемо = we will go / we will set off

In this sentence, Ми підемо туди пішки, the idea is a future action: we will go there on foot.

A useful pattern:

• я піду = I will go
• ти підеш = you will go
• він/вона піде = he/she will go
• ми підемо = we will go
• ви підете = you will go
• вони підуть = they will go

Because йдемо usually means we are going / we go, not we will go.

Compare:

• Ми йдемо туди пішки. = We are going there on foot.
• Ми підемо туди пішки. = We will go there on foot.

So the sentence uses підемо because it talks about a future decision or plan.

These are all verbs of motion, but they are used differently.

• йти = to be going, to go in one direction, ongoing movement
• піти = to go, to set off, to start going, usually a single completed movement in one direction
• ходити = to go habitually, repeatedly, or in different directions

Examples:

• Я йду додому. = I am going home.
• Я піду додому. = I will go home / I’ll set off home.
• Я ходжу до школи пішки. = I go to school on foot / I walk to school.

In your sentence, підемо comes from піти, because it refers to a future trip to a destination.

Туди means there, but specifically in the sense of to there or toward that place.

This is important:

• там = there, at that place
• туди = there, to that place
• звідти = from there

So:

• Ми будемо там. = We will be there.
• Ми підемо туди. = We will go there.

Since the sentence involves motion, туди is the natural choice.

Пішки means on foot or by walking.

It is an adverb, so it describes how the action is done:

• Ми підемо туди пішки. = We will go there on foot.

English uses a phrase (on foot), but Ukrainian uses a single adverb: пішки.

Other examples:

• Я прийшов пішки. = I came on foot.
• Вона часто ходить пішки. = She often goes on foot / She often walks.

Because пішки is already an adverb, not a noun phrase.

In English, we say on foot, which needs the preposition on.
In Ukrainian, пішки by itself already expresses that idea.

So you say:

• їхати автобусом = to go by bus
• летіти літаком = to fly by plane
• йти пішки = to go on foot

You do not need a separate word meaning on here.

It could be omitted.

Ukrainian often leaves out subject pronouns when the verb already makes the subject clear.

Since підемо clearly means we will go, you can say:

• Ми підемо туди пішки.
• Підемо туди пішки.

Both are correct.
Including ми can add emphasis, clarity, or contrast, for example:

• Ми підемо туди пішки, а вони поїдуть автобусом.
  = We will go there on foot, but they will go by bus.

Yes. Ukrainian word order is fairly flexible.

The neutral order here is:

• Ми підемо туди пішки.

But you could also hear:

• Ми туди підемо пішки.
• Туди ми підемо пішки.
• Пішки ми підемо туди.

The basic meaning stays the same, but the emphasis changes.

For example:

• Туди ми підемо пішки. = There, we’ll go on foot.
• Пішки ми підемо туди. = On foot is how we’ll go there.

So word order in Ukrainian often reflects emphasis rather than strict grammatical necessity.

It can carry both ideas.

Because піти is a perfective verb, it often suggests a single whole action, and very often the idea of setting off or starting to go.

So Ми підемо туди пішки can mean:

• We will go there on foot.
• We will set off there on foot.

In many everyday contexts, English just translates it as will go.

You would normally say:

• Ми йдемо туди пішки.

That uses йдемо, the present-tense form of йти.

So compare:

• Ми йдемо туди пішки. = We are going there on foot.
• Ми підемо туди пішки. = We will go there on foot.

This is a very useful contrast to learn.

A simple pronunciation guide is:

• Ми ≈ my (but with a shorter, less diphthong-like vowel)
• підемо ≈ pee-DEH-mo
• туди ≈ too-DY
• пішки ≈ PEESH-ky

A rough full pronunciation:

my pee-DEH-mo too-DY PEESH-ky

A couple of notes:

• и in Ukrainian is not the same as English ee. It is a shorter, more central vowel.
• і is closer to English ee.
• шк in пішки is pronounced clearly: peesh-ky.

Yes, very naturally.

Since пішки means on foot, English often translates the whole sentence as:

• We’ll walk there.

That is often the most natural English version, even though the Ukrainian structure is literally closer to:

• We will go there on foot.

So both are good ways to understand it.