Andrei este aici de două zile.

Romanian often uses the present tense for a situation that began in the past and is still true now.

So:

• Andrei este aici de două zile
  literally looks like Andrei is here for two days
• but in natural English it means Andrei has been here for two days

This is a very common pattern in Romanian:

• Sunt aici de o oră = I have been here for an hour
• Locuiește aici de trei ani = He/She has lived here for three years

So the present tense in Romanian can match the English present perfect when the action or state still continues.

Here, de două zile expresses duration up to the present.

In this sentence, it means:

• for two days
• or more exactly, for the last two days / since two days ago

The word de is very commonly used in Romanian with time expressions like this:

• de o săptămână = for a week
• de trei luni = for three months
• de mult timp = for a long time

So este aici de două zile means that Andrei arrived two days ago and is still here now.

Because zi is a feminine noun, and the Romanian word for two changes depending on gender:

• doi for masculine nouns
• două for feminine nouns

Examples:

• doi băieți = two boys
• două fete = two girls
• două zile = two days

So două zile is correct because zile comes from zi, which is feminine.

Because the sentence refers to two days, so the noun must be in the plural:

• o zi = one day
• două zile = two days

This is normal Romanian number agreement: after numbers greater than one, the noun is generally plural.

No, they are usually not the same.

• de două zile = for two days up to now, continuing from the past into the present
• pentru două zile = for two days as a planned duration, purpose, or limited period

Compare:

• Andrei este aici de două zile = Andrei has been here for two days
• Andrei vine aici pentru două zile = Andrei is coming here for two days

So in your sentence, de is the correct choice because it describes an ongoing situation.

Yes. E is the short, very common spoken form of este.

So both are correct:

• Andrei este aici de două zile
• Andrei e aici de două zile

The version with este is a bit fuller and slightly more formal or careful.
The version with e is extremely common in everyday speech.

Yes, Romanian word order is somewhat flexible, but the most neutral and natural order here is:

• Andrei este aici de două zile

This is:

• subject: Andrei
• verb: este
• place: aici
• duration: de două zile

You may sometimes hear variations for emphasis, but they are less neutral. For a learner, this standard order is the safest one to use.

Because Romanian usually does not use an article in this kind of time expression.

You simply say:

• de două zile
• de o săptămână
• de trei ani

Adding an article would sound wrong here. This is just the normal Romanian way to express duration.

Aici is pronounced roughly like ah-EECH.

More carefully, it is approximately:

• a as in father
• ici with a sound like eech, where ci before no extra vowel gives a ch sound

So the whole word is close to ah-EECH.

The whole sentence is approximately:

• Andrei yess-teh ah-EECH deh DOH-uh ZEE-leh

That is only an approximation, but it is good enough to get started.

Yes. That is an important part of the meaning.

Because Romanian uses:

• a present-tense verb: este
• plus a duration expression: de două zile

the sentence implies that the situation is still true now.

So Andrei este aici de două zile means:

• he came here two days ago
• and he has not left yet

If you wanted to say he was here for two days but is not here anymore, Romanian would normally use a past form instead.

A natural way would be:

• Andrei a fost aici două zile = Andrei was here for two days

This does not necessarily mean he is still here.

So the contrast is:

• Andrei este aici de două zile = he has been here for two days, and still is
• Andrei a fost aici două zile = he was here for two days

This difference is one of the most useful things to notice in the original sentence.