Learn Hardcore Latin: Filia respondet: "Librum lego, quia foris dies frigidus est." - The daughter answers: "I am reading a book, because outside the day is cold."

Liber is the dictionary (nominative) form meaning book.
In the sentence, librum is the direct object of lego (I read / I am reading), so it must be in the accusative case.

nominative (subject): liber – the book (does something)
accusative (object): librum – I read the book

Latin marks the role in the sentence with endings, not with word order.

Where is the word I in librum lego?

Latin usually leaves out subject pronouns if the verb ending already shows the person.

lego = I read / I am reading (1st person singular)
The -o ending tells us the subject is I (ego), so ego is understood and not written.

So librum lego literally means [I] read a/the book.

What tense are respondet and lego, and how do they translate into English?

Both respondet and lego are present tense.

respondet = she responds / she is responding
lego = I read / I am reading

Latin has only one present tense form, which can cover both English and depending on context.