Ne lector quidem omnia uno die meminisse potest; ideo cotidie legere utile est.

Together, ne ... quidem means not even. Latin usually places the word or phrase being emphasized between ne and quidem.

So:

• ne lector quidem = not even the reader

This split construction is normal and very common in Latin.

Because ne ... quidem is a set idiom meaning not even. Ordinary non simply negates a word or clause, but ne ... quidem adds the idea of surprise or emphasis: not even X.

So the sentence is not just saying the reader cannot remember everything; it is stressing that even the reader cannot do it.

Because lector is the subject of potest.

The basic structure is:

• lector ... potest = the reader is able / can

Since the reader is the one who can or cannot remember, Latin puts lector in the nominative case.

Omnia is neuter plural and means all things or everything.

That fits the sentence, because the idea is remember everything, not remember all people.

Compare:

• omnia = everything / all things
• omnes = all people or masculine/feminine plural all

So omnia is the correct form here.

After potest, Latin normally uses an infinitive:

• potest legere = he/she can read
• potest meminisse = he/she can remember

So meminisse is the infinitive that goes with potest.

The whole part:

• omnia ... meminisse potest = can remember everything

This is a special feature of the verb memini. It is a defective verb whose perfect forms have a present meaning.

So:

• memini = I remember
• meminisse = to remember

Even though the form looks perfect, the meaning is not to have remembered here. That is just how this verb works.

That is a very good question. Memini can take either the genitive or the accusative, depending on usage.

The accusative is especially common with:

• neuter pronouns or adjectives such as id, haec, multa, omnia
• things remembered in a more direct way

So omnia meminisse is perfectly normal Latin for to remember everything.

Because Latin often uses the ablative without a preposition to express time within which.

So:

• uno die = in one day / within one day

This is different from an accusative of duration:

• unum diem = for one day

Here the meaning is within the space of one day, so uno die is the standard choice.

Ideo means therefore, for that reason, or that is why.

It connects the second idea to the first:

• No one can remember everything in one day; therefore, reading every day is useful.

So ideo shows the logical result of the first statement.

Yes. Cotidie and quotidie are variant spellings of the same adverb, meaning daily or every day.

In this sentence, it is an adverb modifying legere:

• cotidie legere = to read every day

Yes. In Latin, an infinitive can act like a noun.

So:

• legere = to read or reading
• legere utile est = to read is useful

Natural English usually says:

• it is useful to read

But Latin does not need a dummy it. The infinitive itself functions as the subject.

When an infinitive is the subject, Latin commonly uses a neuter singular predicate adjective.

So:

• legere utile est = literally to read is useful

The infinitive idea is treated as a neuter singular thing, so utile is neuter singular.

If the subject were a feminine noun such as lectio (reading as a noun), you would expect:

• lectio utilis est = reading is useful