Una abeja se acercó a la mesa, pero la avispa se fue enseguida.

Because acercarse is the usual verb here for to come near / to approach.

• acercar by itself is usually to bring something closer
  • Acercó la silla a la mesa = He/She moved the chair closer to the table
• acercarse means to move oneself closer
  • La abeja se acercó a la mesa = The bee approached the table

So the se is part of the verb acercarse, not a separate word you can freely remove here.

In this sentence, both verbs are being used in their pronominal forms:

• acercarse = to approach / come closer
• irse = to go away / leave

That means the se belongs to the verb.

Compare:

• fue = he/she went
• se fue = he/she left / went away

So la avispa se fue sounds more like the wasp went off / left, not just went.

They are both in the preterite (also called the simple past).

• se acercó = approached
• se fue = left / went away

Spanish uses the preterite here because these are seen as completed actions in the past.

The verb acercarse normally uses a before the place or thing approached:

• acercarse a la ventana = to approach the window
• acercarse al perro = to go near the dog
• acercarse a la mesa = to approach the table

So a is required by the verb here.

This is the contrast between the indefinite article and the definite article.

• una abeja = a bee
• la avispa = the wasp

A likely reason is that the bee is being introduced as one bee, while the wasp is being treated as a specific wasp in the situation.

This kind of article choice is very normal in Spanish and depends on context, just as in English.

Because both nouns are grammatically feminine:

• la abeja
• la avispa

They refer to insects, but grammatical gender in Spanish does not always mean biological sex. A noun can be feminine even if the actual animal’s sex is unknown.

That is why the sentence uses:

• una abeja
• la avispa

Enseguida means something like:

• right away
• immediately
• straight away

So:

• la avispa se fue enseguida = the wasp left right away

In Spain, enseguida is very common. Depending on context, it can sometimes mean very soon, but here it clearly means immediately / at once.

Because irse and ir are not exactly the same in meaning.

• ir = to go
• irse = to leave / go away

So:

• La avispa fue on its own would sound incomplete or unusual here
• La avispa se fue clearly means The wasp left

In many situations, English uses go, but Spanish prefers irse when the idea is departing.

Pero means but, so it introduces a contrast:

• A bee approached the table, but the wasp left immediately

If you used y (and), it would just join two actions without highlighting the contrast:

• Una abeja se acercó a la mesa y la avispa se fue enseguida

That is grammatical, but pero better shows the opposite behavior of the two insects.

The accent mark shows both pronunciation and meaning.

• acercó = he/she approached or it approached
• acerco = I bring closer / I approach in the present

So the accent helps distinguish:

• yo acerco = I bring closer
• él/ella se acercó = he/she approached

It also tells you the stress falls on the last syllable: a-cer-CÓ.

In Spanish, it is normal to put a comma before pero when it links two clauses:

• Una abeja se acercó a la mesa, pero la avispa se fue enseguida.

This works much like English:

• A bee approached the table, but the wasp left immediately.

So the comma is standard punctuation here.

No, that would sound wrong here.

Without se, acercar usually needs a direct object, because it means to move something closer:

• La abeja acercó la hoja a la mesa = The bee moved the leaf closer to the table

But if you mean the bee itself moved closer, Spanish uses acercarse:

• La abeja se acercó a la mesa

So the se is necessary for the intended meaning.

Yes. Enseguida adds the idea of speed or immediacy.

• se fue = left
• se fue enseguida = left immediately / left right away

So the sentence not only says that the wasp left, but also that it did so very quickly.