Мама сказала, что если уж я всё равно дома, то могу хотя бы дочитать книгу и пораньше лечь спать.

Because что introduces reported speech or a content clause: said that ...

So Мама сказала, что ... means Mom said that ...

A very common contrast is:

• Мама сказала, что я дома. = Mom said that I am at home.
• Мама сказала: ... = Mom said: ...

So here что is the normal way to connect сказала with the rest of the sentence.

This is the standard if ... then ... pattern:

• если = if
• то = then

So:

• если уж я всё равно дома, то могу ...

literally has the structure if ..., then ...

In Russian, то is often optional, but it is very common, especially when the sentence is a bit long. It makes the logic clearer and can sound more natural.

Уж here is a particle. It does not have a neat one-word English equivalent.

In если уж ..., it adds emphasis and a kind of resigned logic, something like:

• if after all
• if anyway
• seeing as
• since, as it happens

So если уж я всё равно дома has a feel like:

• if I’m home anyway
• seeing as I’m home anyway
• since I’m home anyway

It often gives the sentence a slightly emotional or pragmatic tone rather than changing the core meaning.

Here всё равно means anyway / in any case / all the same.

So я всё равно дома means something like I’m at home anyway.

This is important because всё равно can also mean:

• it’s all the same to me
• I don’t care
• it makes no difference

But in this sentence, it is not about indifference. It is about the situation already being the case: since I’m at home anyway.

Because дома means at home.

Compare:

• дома = at home
• домой = homeward, to home
• в доме = in the house/building

So:

• Я дома. = I’m at home.
• Я иду домой. = I’m going home.
• Я в доме. = I’m in the house/building.

For the idea of someone being at home as a normal personal state/location, Russian usually uses дома, not в доме.

Because дочитать means to finish reading something, to read it to the end.

It is formed from:

• читать = to read
• дочитать = to finish reading

The prefix до- often gives the idea of reaching the end or completing something.

So:

• читать книгу = read a book / be reading a book
• дочитать книгу = finish the book

Here that makes perfect sense: the mother is suggesting not just reading in general, but finishing the book.

Because the sentence is talking about a single completed result: finishing the book.

In Russian:

• читать is imperfective: process, duration, repetition
• дочитать is perfective: completion, one whole finished action

After a modal like могу, Russian often uses a perfective infinitive when the point is being able to complete something:

• могу дочитать книгу = I can finish the book

If the sentence had читать, it would focus more on the activity itself, not the completed result.

Хотя бы means at least.

It sets a minimum acceptable action, often with the feeling:

• if nothing else
• at the very least
• you could at least ...

So могу хотя бы дочитать книгу means something like:

• I can at least finish the book

It suggests that this is not a huge demand; it is presented as the minimum reasonable thing to do.

Because лечь is perfective and fits a one-time action: to lie down / go to bed on this specific occasion.

Compare:

• лечь = perfective, one completed act
• ложиться = imperfective, process/habit/repeated action

So:

• Я обычно ложусь спать в 11. = I usually go to bed at 11.
• Сегодня я лягу спать пораньше. = Today I’ll go to bed earlier.

In this sentence, the mother is talking about what the person could do this time, so лечь спать is natural.

Пораньше means a bit earlier / somewhat earlier.

Compare:

• раньше = earlier
• пораньше = a little earlier, nice and early, earlier than usual

That по- often softens or moderates a comparative in colloquial Russian:

• побольше = a bit more
• получше = a bit better
• пораньше = a bit earlier

So пораньше лечь спать sounds natural and conversational: go to bed a bit earlier.

Because мочь is a modal verb, and modal verbs in Russian normally take an infinitive:

• могу дочитать
• могу лечь

Here one могу governs both infinitives:

• могу хотя бы дочитать книгу и пораньше лечь спать

This is like English I can finish the book and go to bed earlier. Russian does not need to repeat могу before the second verb.

It is somewhere between can and could, depending on how naturally you translate it into English.

Russian могу literally means I can, but in context it can also express a practical option or reasonable course of action:

• I can ...
• I could ...
• I might as well ...

In this sentence, it is not only about physical ability. It is more like: since I’m home anyway, I could at least finish the book and go to bed earlier.

Each comma marks a clause boundary.

1. Мама сказала, что ...

   • comma before что because that ... introduces a subordinate clause

2. ... если уж я всё равно дома, то ...

   • the если clause is also subordinate, so it is separated by a comma:
   • если уж я всё равно дома, то могу ...

So the commas are there because the sentence contains clauses inside clauses:

• main clause: Мама сказала
• content clause: что ...
• conditional clause inside that: если ...

That punctuation is standard Russian syntax.