У ворот парка стоит мама, а за воротами начинается длинная аллея.

The dictionary form is ворота. This noun is plural-only in Russian, like English gates.

After the preposition у meaning by / near / at, Russian uses the genitive case.
So:

• dictionary form: ворота
• genitive plural: ворот

That gives у ворот.

Because ворота парка means the park’s gates or the gates of the park.

In Russian, one noun often modifies another by using the genitive:

• парк = park
• парка = of the park

So у ворот парка literally means by the gates of the park.

Because different prepositions require different cases.

Here the same noun ворота appears with two different prepositions:

• у
  • genitive → у ворот
• за
  • instrumental (for location) → за воротами

So the form changes because the case changes.

Here за means behind / beyond / on the other side of and describes location, not movement.

When за describes location, it normally takes the instrumental case.
The instrumental plural of ворота is воротами.

So:

• за воротами = beyond the gates / behind the gates

If you were talking about motion to a place beyond the gates, Russian would typically use за with the accusative instead.

Yes.

With places like parks, schools, yards, or stadiums, за воротами often means beyond the gates or on the other side of the gates, not necessarily physically hidden behind them.

In this sentence, beyond the gates is the most natural English interpretation.

Russian word order is flexible.

Starting with У ворот парка puts the location first and sets the scene. Then стоит мама introduces who is there.

So this order is good for description:

• first the place
• then the person

Мама стоит у ворот парка is also correct, but it sounds more neutral and puts more focus on мама.

Because стоять means to stand, and Russian commonly uses it to describe a person’s position.

So стоит мама does not just mean that mother is there; it specifically says that she is standing there.

This is especially natural in Russian because ordinary present-tense statements do not normally use a separate word for is.

Because длинная аллея is the subject of the verb.

• аллея = alley, avenue, tree-lined path
• длинная аллея = a long alley

The subject is in the nominative case, so аллея stays nominative, and the verb agrees with it:

• аллея = feminine singular
• начинается = 3rd person singular

So the structure is literally a long alley begins.

Because the verb here is начинаться, which means to begin / to start in the sense that something itself begins.

Compare:

• начинать = to begin something
  
  • Он начинает урок = He begins the lesson
• начинаться = to begin, to start
  
  • Здесь начинается лес = The forest begins here

So начинается длинная аллея means a long alley begins there.

А often links two ideas with a light contrast or a shift of attention.

In this sentence it is not a strong but. It is more like:

• and
• while
• whereas

It connects two parts of the scene:

• mother is standing at the gates
• beyond the gates, a long alley begins

So а marks a gentle contrast or transition.

Because adjectives in Russian must agree with the noun they describe.

Here the noun is аллея, which is:

• feminine
• singular
• nominative

So the adjective must also be:

• feminine
• singular
• nominative

That gives длинная аллея.

Normally, yes. Ворота is a plural-only noun in standard Russian.

So even when English might say the gate, Russian often still uses ворота.

If you mean a small gate or wicket gate, Russian often uses калитка, which is a normal singular noun.

Russian has no words exactly like English the and a.

Instead, definiteness and indefiniteness come from:

• context
• word order
• the situation
• shared knowledge

Here ворота парка are understood as specific because they belong to a particular park, while длинная аллея is being introduced as part of the scene.