Je vais y penser ce soir.

Because je vais + infinitive is the near future in French. It means I am going to ...

So:

• Je vais penser = I am going to think
• Je pense = I think / I am thinking

In this sentence, Je vais y penser ce soir means the speaker plans to think about it later, this evening.

Here, y replaces à + thing after the verb penser.

The verb penser often works as:

• penser à quelque chose = to think about something

So instead of saying:

• Je vais penser à cela ce soir

French very naturally says:

• Je vais y penser ce soir

Here, y means something like about it.

It actually can. Je vais penser à ça ce soir is understandable and natural in speech.

But French often prefers the pronoun y instead of repeating à ça / à cela when the thing has already been mentioned.

So these are both possible:

• Je vais penser à ça ce soir
• Je vais y penser ce soir

The version with y is more compact and very common.

Not in this sentence.

Y can mean:

• there (a place)
  
  • J’y vais = I’m going there
• to it / about it after certain verbs that take à
  • J’y pense = I’m thinking about it

In Je vais y penser ce soir, y does not refer to a place. It refers to a thing or idea already mentioned.

In French, object pronouns usually go before the infinitive when that infinitive is closely connected to another verb.

So:

• Je vais penser à cela
  becomes
• Je vais y penser

You do not say:

• Je vais penser y ❌

This word order is something learners just need to get used to:

• Je vais le faire
• Je vais en parler
• Je vais y penser

French makes an important distinction:

• penser à = to think about
• penser que = to think that
• sometimes penser alone can mean to think in a general sense

Examples:

• Je pense à mon travail. = I’m thinking about my work.
• Je pense qu’il a raison. = I think he is right.

In your sentence, the meaning is to think about something, so French uses penser à, and that is why y can replace the à + thing.

Yes. You could also say:

• J’y penserai ce soir.

That means essentially the same thing: I’ll think about it tonight.

The difference is mostly one of style and nuance:

• Je vais y penser ce soir = very common, conversational, often suggests an intended future action
• J’y penserai ce soir = also common, a bit more direct as a future statement

Both are correct.

Ce soir means this evening or tonight, depending on context.

Examples:

• Je le fais ce soir. = I’m doing it tonight.
• On sort ce soir. = We’re going out tonight.

In your sentence, ce soir tells you when the speaker is going to think about it.

It can match either one in English, depending on context.

Word-for-word, it is closer to:

• I’m going to think about it tonight

But in natural English, the best translation might also be:

• I’ll think about it tonight

French aller + infinitive is very common and often overlaps with what English expresses using will.

Usually no, or at least not in standard usage for a direct personal reference.

Y normally replaces:

• à + thing
• or a place

So:

• Je pense à mon problème → J’y pense
• Je vais à Paris → J’y vais

But if you mean thinking about a person, French usually keeps the full phrase:

• Je pense à Marie
  not usually
• J’y pense for Marie

So in your sentence, y most naturally refers to an idea, subject, problem, suggestion, etc.

A careful pronunciation is roughly:

Zhuh veh zee pahn-say suh swahr

A few helpful points:

• Je sounds like zhuh
• vais sounds like veh
• y sounds like ee
• penser ends with the -er sound pronounced like ay
• ce soir sounds roughly like suh swahr

Also, in normal speech, it flows smoothly:

• Je vais y penser ce soir

Yes, but it is slightly different in tone.

• penser à = to think about
• réfléchir à = to think over / consider / reflect on

So:

• Je vais y penser ce soir = I’m going to think about it tonight
• Je vais réfléchir à ça ce soir = I’m going to think it over tonight

The second version can sound a little more deliberate or thoughtful.