Min nye lejlighed ligger tæt på universitetet.

Because lejlighed is a common-gender noun in Danish.

• en lejlighed = an apartment
• common gender takes min
• neuter nouns take mit

So:

• min lejlighed = my apartment
• but mit hus = my house

Because the adjective comes after a possessive word: min.

In Danish, when an adjective describes a noun that is made definite by a possessive like min, din, hans, hendes, vores, the adjective usually takes -e.

So:

• en ny lejlighed = a new apartment
• min nye lejlighed = my new apartment

This is similar to how the noun is understood as specific: not just any apartment, but my apartment.

Because Danish normally does not use the suffixed definite article when there is already a possessive.

Compare:

• lejligheden = the apartment
• min lejlighed = my apartment

You usually do not say min lejligheden.

So the possessive min already makes the noun definite enough.

In Danish, ligge is very commonly used to talk about where places are located.

So:

• Lejligheden ligger tæt på universitetet. = The apartment is located close to the university.

This is often more natural in Danish than using er.

A rough distinction:

• er = is
• ligger = lies / is situated / is located

For buildings, towns, streets, and geographical places, ligger is extremely common.

Yes, tæt på functions together as an expression meaning close to.

Examples:

• tæt på universitetet = close to the university
• tæt på centrum = close to downtown/the center

You can think of it as:

• tæt = close/tight
• på = on/to

But in this sentence, it is best learned as the fixed expression tæt på = close to.

Because universitetet is the definite form of universitet.

• et universitet = a university
• universitetet = the university

Since the sentence refers to a specific university, Danish uses the definite form.

This is very common in Danish: instead of a separate word like English the, Danish often adds the definite ending directly to the noun.

Universitet is a neuter noun.

You can see that from:

• et universitet = a university

Its definite singular form is:

• universitetet = the university

For many neuter nouns, the definite ending is -et.

Compare:

• et hus → huset
• et universitet → universitetet

The basic structure is:

• Min nye lejlighed = subject
• ligger = verb
• tæt på universitetet = adverbial phrase of location

So the sentence follows normal Danish main-clause word order:

Subject + verb + other elements

That is the same basic pattern as in English:

My new apartment + is located + close to the university

Yes, that is understandable and grammatically fine.

However, ligger tæt på is often more natural when talking about the physical location of a home or building.

So:

• Min nye lejlighed ligger tæt på universitetet = very natural
• Min nye lejlighed er tæt på universitetet = also correct, but slightly less specifically about location

Yes, lejlighed is a word many learners find tricky.

A rough guide is:

• lej- sounds somewhat like English lie
• -lig- is reduced and lighter than it looks
• -hed often sounds like a soft ending, not strongly pronounced

The stress is usually on the first syllable: LEJ-lig-hed

A very rough English-style approximation is:

LYE-lee-hed or LYE-li-hed

But the real Danish pronunciation is more compressed and softer than that, especially in the middle and final parts.

You usually put ikke after the verb in a main clause.

So:

• Min nye lejlighed ligger ikke tæt på universitetet. = My new apartment is not close to the university.

This follows normal Danish word order for negation in main clauses:

subject + verb + ikke + rest

Yes. In a Danish main clause, the finite verb normally stays in second position.

So if you move Tæt på universitetet to the front, the verb must come before the subject:

• Tæt på universitetet ligger min nye lejlighed.

That is correct, though it sounds more marked or literary than the neutral version.

Compare:

• Min nye lejlighed ligger tæt på universitetet. = neutral
• Tæt på universitetet ligger min nye lejlighed. = emphasis on the location