À l'est de la maison, il y a un petit jardin.

In French, est (east) is treated as a noun and normally needs a definite article:

• l'est = the east (from le est → l'est)

When you add the preposition à (at / to / in) before l'est, you get:

• à + l'est → à l'est = to the east / in the east / east of

So you can’t say à est because you’re missing the article.
The full idea is à l’est (de quelque chose) = to the east (of something).

Yes, the accent is required.

• À (with accent) is the preposition à meaning at, in, to.
• A (without accent) would be the verb form a (3rd person singular of avoir = has).

At the beginning of a sentence, it’s capitalized as usual: À.
You must always write the accent, even on capital letters in good French.

French normally uses:

• l’est (lowercase) when you mean the direction east (as in this sentence).
• l’Est (capital E) when you mean a specific region or geopolitical concept, like l’Est de la France (the East of France) or l’Est vs l’Ouest in politics/history.

In À l'est de la maison, you’re just giving a direction relative to the house, so est stays lower-case.

Il y a is a fixed French expression that means there is / there are.

Literally, it’s built from:

• il = dummy subject pronoun (like “it” in “it’s raining”)
• y = there
• a = has (3rd person singular of avoir)

Historically it’s like “it has there”, but you should remember it as a unit meaning there is/are:

• Il y a un petit jardin. = There is a small garden.
• Il y a trois chaises. = There are three chairs.

In the negative:

• Il n’y a pas de jardin. = There is no garden.

Both word orders are possible:

• À l'est de la maison, il y a un petit jardin.
• Il y a un petit jardin à l'est de la maison.

They mean the same thing. The difference is emphasis:

• Starting with À l'est de la maison highlights the location first.
• Starting with Il y a un petit jardin highlights the existence of the garden first.

The comma after the introductory phrase is normal and helps the rhythm, but in everyday writing you sometimes see it omitted.

Because jardin is a masculine noun in French:

• un jardin = a garden (masculine)
• le jardin = the garden

So the adjective and article must agree in gender:

• masculine: un petit jardin
• feminine: une petite maison

Even if -in endings sometimes feel feminine to English speakers, gender is arbitrary and must be memorized:

• un jardin (m), un matin (m)
• une fin (f), une main (f)

Most French adjectives do come after the noun, but a common group of adjectives often comes before the noun. A popular memory trick is BANGS (Beauty, Age, Number, Goodness, Size).

• petit / grand are size adjectives, so they often go before the noun:
  • un petit jardin
  • un grand jardin
  • une petite maison

Compare:

• un jardin public (a public garden) → adjective public comes after.
• un jardin secret (a secret garden) → adjective secret comes after.

So petit is one of the regular exceptions that go before.

Step by step:

1. maison is feminine: la maison = the house.
2. After de
   • la, there is no contraction:
     • de + la maison → de la maison

You can’t say de le maison because:

• le is the masculine article; maison is feminine, so it must be la.
• de le would contract to du, but that only happens with de + le (masculine).

You also can’t just drop the article and say de maison in this context. You’re talking about a specific house, so you need de la maison = of the house / from the house / east of the house.

In French, when you give a direction relative to something, you normally use:

• à l’est de [noun] = to the east of [noun]

So you need de:

• à l’est de la maison = to the east of the house
• au nord de la ville = to the north of the city
• au sud de Paris = to the south of Paris

Without de, à l’est la maison is incorrect in standard French.

Because of how à combines with the definite article:

• le est → l’est (elision before a vowel)
• With à:
  • à + le usually → au (e.g. au jardin)
  • but when the article is l', you get à l':
    • à + l’hôtel → à l’hôtel
    • à + l’école → à l’école
    • à + l’est → à l’est

So the correct form is à l’est, not au est.

Approximate pronunciation (in IPA):

• À l'est de la maison → /a lɛst də la mɛ.zɔ̃/
• il y a un petit jardin → /il j‿a œ̃ pə.ti ʒaʁ.dɛ̃/

Some points:

• À l’est: there is a liaison: l’est is /lɛst/, and with de it sounds like l’est de /lɛstə/.
• de la: each word clearly pronounced /də la/.
• maison: nasal vowel at the end /mɛ.zɔ̃/ (the n is not pronounced as a full consonant).
• il y a: flows together /ilj‿a/.
• un: nasal vowel /œ̃/.
• petit before a consonant (like jardin) is often pronounced /pə.ti/ with silent t; you generally do not pronounce the t here.
• jardin: /ʒaʁ.dɛ̃/ with another nasal vowel at the end.

That would sound incomplete or poetic/elliptical at best. In normal French, you need a verb:

• À l'est de la maison, il y a un petit jardin.

Without il y a, À l'est de la maison, un petit jardin is missing the main verb and would not be considered a correct standard sentence in regular prose or conversation.

You could say À l’est de la maison or À l’est de la maison il y a….
The version De la maison à l’est, il y a un petit jardin is understandable but sounds awkward and unnatural for this meaning.

If you want to keep it natural, stick to:

• À l’est de la maison, il y a un petit jardin.
• Il y a un petit jardin à l’est de la maison.