Learn Hardcore Russian: На совещании начальница уточнила срок проекта и спросила, есть ли у нас запас времени. - At the meeting, the boss clarified the project deadline and asked whether we have a time reserve.

на совещании = at/in the meeting (as an event)
You’d use в + Prepositional more for being physically inside a place/container (e.g., в комнате, в офисе), though even with meetings, на is the default.

What case is совещании in, and how do I know?

совещании is Prepositional singular of совещание. The clue is the preposition на meaning at/on, which (with location) requires the Prepositional case:

на совещании (where?) → Prepositional

Why is начальница used here—what nuance does it have compared to начальник?

начальница is the feminine form meaning female boss/manager/supervisor.

начальник can be male, or sometimes used generically (depending on context and speaker), but начальница clearly marks the boss as a woman.
It’s a normal, common word; tone depends on context, but it’s not automatically informal or rude.

What’s the difference between уточнила and спросила? Aren’t they both “asked”?

They’re related but not the same:

уточнила (from уточнить, perfective) = clarified / уточнила детали → she made the deadline more precise, confirmed specifics.
спросила (from спросить, perfective) = asked (a question) → she requested information directly.
So she first clarified the project deadline, then asked whether we have any time buffer.

Why is it срок проекта—what case is проекта and what does it mean?

проекта is Genitive singular of проект. The genitive often shows relationships like “X of Y”:

срок проекта = the project’s deadline/timeframe (literally “the term/period of the project”).
In modern workplace Russian, срок can mean deadline or timeframe, depending on context.

Why is срок not changed—shouldn’t it be some special form as an object?

It is in the object position, but срок is inanimate masculine, and in Russian the Accusative = Nominative for inanimate masculine nouns:

Nominative: срок
Accusative: срок (same form)
So it looks unchanged even though it’s the direct object of уточнила.

What is the structure спросила, есть ли у нас… and why is there a comma?

This is an indirect question (reported speech). Russian introduces it with ли and separates it with a comma:

спросила, есть ли… = she asked whether…
The comma is required because the clause есть ли у нас запас времени is a subordinate clause dependent on спросила.

What exactly does ли do, and where can it go?

ли is a particle that marks a yes/no question inside a larger sentence, often translated as whether/if. It usually comes right after the word being “questioned”:

есть ли… = whether there is/are…
You’ll also see patterns like:
спросил, будет ли… (asked whether it will…)
спросила, можем ли мы… (asked whether we can…)
It normally cannot stand at the very beginning of the clause by itself.

Why is есть included here—can it be omitted?

Often, yes. Russian frequently omits есть (“there is/are”) in the present tense:

спросила, есть ли у нас запас времени
спросила, есть ли у нас запас времени → sounds neutral/explicit
спросила, есть ли у нас запас времени is standard; but you may also hear спросила, есть ли у нас запас времени with есть kept for clarity.
In many contexts you could say спросила, есть ли у нас запас времени or even спросила, есть ли у нас запас времени—but with ли, есть is very common and natural.

What does у нас mean grammatically? Why not a verb like “to have”?

Russian commonly expresses possession with у + Genitive + (optional) есть:

у нас (есть) = we have (literally “by/at us there is”)
Here нас is Genitive after у. So:
есть ли у нас запас времени = whether we have a time buffer

What is запас времени—what case is времени, and what does the phrase mean?

запас времени literally means a запас (reserve/buffer) of time → time buffer / extra time / slack.
времени is Genitive singular of время (an irregular noun). Genitive is used after nouns like запас to show “a supply of X”:

запас чего? → времени
So the phrase is “a reserve of time,” i.e., extra time available.