Папа сказал, что уголь уже готов, и можно поджарить овощи на решётке.

Because папа is one of the Russian nouns that refer to a male person but have an -а / -я ending. A few common examples are:

• папа = dad
• дядя = uncle
• мужчина = man
• юноша = युवक / young man

These nouns decline like many feminine nouns, but they are grammatically masculine in agreement. That is why the past-tense verb is сказал, not сказала.

So:

• папа сказал = dad said
• not папа сказала

Сказал is from сказать, the perfective verb. It usually refers to one completed act of saying.

Here that fits well: dad said something once, and the statement is presented as a completed event.

• сказал = said / told
• говорил = was saying / used to say / spoke

So Папа сказал... sounds like a normal narrative sentence: Dad said...

If you used говорил, the meaning would shift more toward an ongoing or repeated action.

Here что is a conjunction meaning that. It introduces the content of what was said.

• Папа сказал, что...
• Dad said that...

So the structure is:

• Папа сказал = Dad said
• что уголь уже готов = that the charcoal is already ready

This is a very common pattern in Russian.

Literally, уголь can mean coal or charcoal depending on context. In a grilling sentence like this, it usually means charcoal or the coals.

So in this context, a natural English understanding is something like:

• the charcoal is ready
• the coals are ready

Russian often uses уголь in the singular as a mass noun.

Готов is the short form of the adjective готовый.

Russian often uses the short form when the adjective is part of the predicate, especially for a temporary state:

• уголь готов = the charcoal is ready

Compare:

• готовый уголь = ready charcoal
• уголь готов = the charcoal is ready

So here готов is correct because it describes the current state of the charcoal.

Уже means already.

So:

• уголь уже готов = the charcoal is already ready

It suggests that the charcoal has reached the right stage by now, perhaps sooner than expected or at least at the needed moment.

Russian word order is flexible, but уже is very naturally placed before the part it closely relates to:

• уголь уже готов

Because можно is an impersonal word. It means something like:

• it is possible
• one can
• you can
• we can
  depending on context

So можно поджарить овощи literally means:

• it is possible to grill the vegetables

In natural English, this often becomes:

• we can grill the vegetables
• you can grill the vegetables now

Russian does this very often: it leaves the doer unspoken when it is general or obvious from context.

Поджарить is perfective, while жарить is imperfective.

After можно, either aspect is possible, but the choice changes the feel:

• можно поджарить = you can grill/fry them now, as a complete action
• можно жарить = you can be grilling / it is possible to grill, with more focus on the process or activity

Here поджарить sounds natural because the speaker is talking about a concrete next step: the charcoal is ready, so now the vegetables can be grilled.

Also, поджарить often suggests browning or grilling something until it’s nicely cooked.

It is in the accusative plural, because it is the direct object of поджарить.

• поджарить что? = to grill/fry what?
• овощи = vegetables

For inanimate plural nouns, the accusative form is usually the same as the nominative form. That is why овощи looks unchanged here.

So although the form is the same, its role in the sentence is accusative.

Because на with a location usually takes the prepositional case.

• решётка = grate / grill rack
• на решётке = on the grate

Here the idea is location: the vegetables are cooked on the grill grate.

Compare:

• на решётке = on the grate
• на решётку = onto the grate

So the case changes depending on whether the meaning is location or direction.

Also, note the letter ё in решётке. It is pronounced, and it is always stressed:

• решётка
• roughly: rye-SHYOT-ka

As written, the sentence presents two pieces of reported information after Папа сказал:

• что уголь уже готов
• (что) можно поджарить овощи на решётке

In other words, the second что is understood but omitted.

You can think of the full structure as:

• Папа сказал, что уголь уже готов, и что можно поджарить овощи на решётке.

Russian often omits the repeated что, but the comma still helps separate the clauses.

So the comma before и is tied to the sentence structure, not just to a simple list of words.