Vamos plantar uma horta perto de casa.

It can mean either, depending on context.

• Vamos + infinitive can be a suggestion: Let’s plant
• It can also express a near future: We’re going to plant

So Vamos plantar uma horta perto de casa could mean either:

• Let’s plant a vegetable garden near home
• We’re going to plant a vegetable garden near home

In everyday speech, both readings are very common. Context usually makes it clear.

Portuguese often leaves out subject pronouns when the verb form already shows who the subject is.

• Vamos already tells you the subject is we
• So (Nós) vamos plantar... and Vamos plantar... are both correct

Leaving out nós sounds very natural in Brazilian Portuguese.

Because Portuguese normally uses ir + infinitive directly, without a.

• vamos plantar
• vou estudar
• eles vão viajar

This is different from Spanish, which uses ir a + infinitive.

So an English speaker who also knows Spanish may expect vamos a plantar, but in Portuguese that is not the normal structure here.

Horta is a feminine noun meaning a vegetable garden, kitchen garden, or sometimes a small garden for vegetables and herbs.

That is why the sentence uses:

• uma horta

not um horta

Related words:

• jardim = garden, usually ornamental
• quintal = backyard / yard
• horta = a place where you grow vegetables, herbs, etc.

Because Portuguese often uses an article where English might not.

• uma horta = a vegetable garden

Using uma sounds natural when introducing it as one thing you plan to make or plant.

You may sometimes hear article omission in certain styles or headlines, but in normal speech uma horta is the standard, natural choice.

Perto de is a fixed expression meaning near or close to.

So:

• perto de casa = near home
• perto da escola = near the school
• perto do supermercado = near the supermarket

You normally do not say just perto casa. The de is part of the structure.

This is an important and very common point.

With casa, Portuguese often omits the article when it means home in a general, personal sense.

• perto de casa = near home
• em casa = at home
• de casa = from home / of home, depending on context

But when you mean a specific house/building, you usually use the article:

• perto da casa = near the house

So:

• perto de casa sounds like near home
• perto da casa sounds more like near the house

Yes, plantar uma horta is natural in Portuguese.

Portuguese commonly uses plantar with things you grow, so this phrase works well. You may also hear:

• fazer uma horta = make/start a vegetable garden
• montar uma horta = set up a vegetable garden

All of these can be natural, but plantar uma horta is perfectly normal and easy to understand.

Yes, but the original order is very natural.

Standard version:

• Vamos plantar uma horta perto de casa.

Possible variations:

• Perto de casa, vamos plantar uma horta.
• Vamos perto de casa plantar uma horta.
  This is less natural in many contexts.

Portuguese allows some flexibility, but the original sentence is the most straightforward and neutral.

It depends on context.

Casa without a possessive often means home in a broad sense. So perto de casa can mean:

• near my home
• near our home
• near home

The exact owner is usually understood from the situation, not from the word itself.

A broad Brazilian-style pronunciation would sound roughly like:

• VAH-mus plan-TAR OO-ma OR-ta PEHR-tu dji KAH-zah

A few useful notes:

• vamos: the a is open, and the final -os is usually a light us sound in many Brazilian accents
• horta: the h is silent
• perto de: the de often sounds like dji before a vowel in many Brazilian accents
• casa: the s between vowels sounds like z

So casa sounds more like KAH-zah than KAH-sah in Brazilian Portuguese.