Večer budeme sedět nahoře u lampy a babička dole v kuchyni připraví čaj.

Yes, both are future, but Czech forms the future differently depending on aspect.

• sedět is imperfective (to be sitting / to sit as an ongoing state), so its future is made with být
  • infinitive:
    • budeme sedět = we will be sitting
• připravit is perfective (to prepare, to get done as a completed action), so Czech usually uses the present-looking form to express future:
  • připraví = she will prepare

So:

• budeme sedět = future of an imperfective verb
• připraví = future meaning of a perfective verb

This is one of the most important patterns in Czech verbs.

Because Czech often omits subject pronouns when they are clear from the verb ending.

• budeme already means we will
• so (my) budeme sedět is possible, but my is usually unnecessary

Czech does this a lot:

• budu = I will
• budeš = you will
• budeme = we will

You only add the pronoun if you want emphasis or contrast:

• My budeme sedět, ale oni odejdou.
  • We will sit, but they will leave.

Večer here means in the evening and works as a time expression without a preposition.

Czech often does this with parts of the day or time expressions:

• ráno = in the morning
• večer = in the evening
• v noci = at night

So Večer budeme sedět... is a very natural way to begin a sentence with In the evening...

Grammatically, learners are often told to just treat večer here as a fixed adverbial time expression.

lampy is in the genitive singular because it follows the preposition u.

• u usually means by, near, at
• u takes the genitive

So:

• lampa = lamp
• u lampy = by the lamp / near the lamp

This is a very common preposition-case combination:

• u stolu = by the table
• u okna = by the window
• u domu = by the house

Because v kuchyni means in the kitchen as a location, not movement toward it.

Czech distinguishes between:

• location: v
  • locative
• movement into: do
  • genitive

So:

• v kuchyni = in the kitchen
• do kuchyně = into the kitchen

In this sentence, Grandma is simply located there while preparing tea, so v kuchyni is correct.

Also note the case:

• kuchyně = kitchen
• v kuchyni = locative singular

They are adverbs of place.

• nahoře = upstairs / up above
• dole = downstairs / down below

So the sentence contrasts two locations:

• we will be sitting upstairs
• grandma will prepare tea downstairs in the kitchen

These are very common Czech adverbs and do not need a preposition.

Examples:

• Jsem nahoře. = I’m upstairs.
• On je dole. = He’s downstairs.

čaj is in the accusative singular, because it is the direct object of připraví.

Grandma is preparing what?

• čaj = tea

For masculine inanimate nouns like čaj, the accusative singular is often the same as the nominative singular, so it looks unchanged.

• nominative: čaj
• accusative: čaj

That is normal.

The word order is fairly natural, but Czech word order is more flexible than English.

This sentence is arranged in a very readable way:

• Večer sets the time first
• budeme sedět nahoře u lampy gives the first clause
• a babička dole v kuchyni připraví čaj gives the second clause

Czech word order often depends on focus, emphasis, and information flow, not just strict grammar.

For example, variations are possible, such as:

• Večer budeme nahoře u lampy sedět...
• Babička dole v kuchyni připraví večer čaj...

But the original version sounds natural and balanced.

Because the second clause needs its subject stated clearly.

In the first clause:

• budeme already tells you the subject is we

In the second clause:

• připraví only tells you he/she/it will prepare
• so Czech usually includes the noun or pronoun if it matters who is doing the action

That is why the sentence says:

• babička ... připraví čaj = grandma will prepare tea

Without babička, the subject would only be understood as he/she from the verb ending.

Here u lampy most naturally means by the lamp or near the lamp.

The preposition u usually gives the idea of being next to, by, or at something.

So:

• u lampy = by the lamp / near the lamp

It does not mean under the lamp.
For under, Czech would use pod:

• pod lampou = under the lamp

It can mean both, depending on context, but in this sentence it is best understood as to be sitting.

• sedět often describes a state or position
• so budeme sedět usually means we will be sitting

That matches the ongoing, background action in the sentence, while připraví čaj is the more completed action.

So the contrast is:

• budeme sedět = ongoing situation
• připraví čaj = completed event

Here a simply means and.

It links the two clauses:

• we will be sitting upstairs by the lamp
• and grandma downstairs in the kitchen will prepare tea

In some contexts, a can feel slightly like while if two actions happen at the same time, but the basic meaning is still and.

So in this sentence, it is safest to understand it as a straightforward and.