What is the purpose of “a” in these sentences if not *and*

Question

These are the images from the lessons im taking

Answer 1

I'd say this а is a feature of politeness and/or informality. Perhaps, you don't need to translate it, but you still need to know how to use it, if you don't want to come off as rude in conversations. In a conversation Лена, где Света? would sound too demanding, as if you were commanding Lena to tell you where Sveta was. a, by virtue of its informality, makes this almost oppressive tone go away, turning the question into a more polite/relaxed version.

By the way, it would be interesting to note here that if you were to use и instead of а in this setting, it could come off as more aggressive, not less. Here's the scenario: Маша and Петя are a couple; they are invited to an event and are asked not to be late; Маша arrives on time, but Петя is nowhere to be seen. The host, if they felt Маша was somehow responsible for Петя's absence, could then explode at Маша like this:

Маша, и где Петя?

If the host were to ask Маша, а где Петя?, this is just asking a question, and politely. But Маша, и где Петя? kinda tells Маша off for not making sure Петя was on time.

Answer 2

I believe another function of the interrogative a particle/interjection is akin to the adversative conjunction a in compound sentences.

Like in compound sentences where it contrasts two statements, in interrogation it contrasts the expected state of affairs which doesn't obtain (implicitly or explicitly) with the question it gives rise to.

Thus in the question Лена, а где Света? the interrogative a could mean that Света was expected to be present but is away for some reason.

Another example in a dialogue:

- Вам кого?
- Мне нужна Света.
- Она ушла.
- А когда она вернётся?

Here a contraposes the question to the statement Она ушла negating the expected state of affairs, i.e. Sveta's presence.

And of course А? can function as 1) a standalone interrogative particle meaning What? / What's that? and 2) a reiteration of a question after it's been asked.

1)
- Я сегодня уезжаю. - I'm leaving today.
- А? Что ты сказала? - Huh? ⁵ What did you say?

2) Где ты была вчера вечером, а? - Where were you last night? Huh? ³