Non ho fretta, posso aspettare qui.

Because avere fretta is the normal Italian expression for to be in a hurry. Italian often uses avere (to have) where English uses to be.

So:

• Ho fretta = I’m in a hurry
• Non ho fretta = I’m not in a hurry

This is just an idiomatic pattern you should learn as a chunk: avere fretta.

In the expression avere fretta, Italian normally does not use an article. It is a fixed phrase.

• Ho fretta = correct
• Non ho fretta = correct

Adding an article, like ho la fretta, would sound wrong in this context.

So it is best to remember fretta here as part of the whole expression avere fretta.

In Italian, non usually goes directly before the verb to make it negative.

Examples:

• Ho fretta = I’m in a hurry
• Non ho fretta = I’m not in a hurry

The same rule works in many sentences:

• Parlo italiano = I speak Italian
• Non parlo italiano = I don’t speak Italian

So non ho is the standard word order.

Italian often leaves out subject pronouns because the verb ending already shows who the subject is.

• ho = I have
• posso = I can

So Non ho fretta, posso aspettare qui already clearly means I’m not in a hurry, I can wait here.

You can say Io non ho fretta, posso aspettare qui, but io usually adds emphasis, as if you were saying I’m not in a hurry.

Because potere (can / to be able to) is a modal verb, and modal verbs are followed by an infinitive.

So:

• posso = I can
• aspettare = to wait

Together:

• posso aspettare = I can wait

This is the same pattern as:

• voglio mangiare = I want to eat
• devo andare = I must go
• so nuotare = I know how to swim

Here aspettare means to wait.

In Italian, aspettare can be used:

• without an object: Posso aspettare = I can wait
• with an object: Aspetto Maria = I’m waiting for Maria

This is important because English usually says wait for, but Italian often uses aspettare directly without a word for for.

So:

• Aspetto l’autobus = I’m waiting for the bus
• Posso aspettare qui = I can wait here

Qui means here.

Yes, you can often use qui and qua interchangeably in everyday Italian. In many situations, the difference is very small or nonexistent.

So both of these sound natural:

• Posso aspettare qui
• Posso aspettare qua

Very roughly, some speakers may feel a tiny stylistic difference, but for most learners it is fine to treat them as equivalents.

The comma separates two closely related ideas:

• Non ho fretta
• posso aspettare qui

In natural English, you might also split them into two sentences:

• Non ho fretta. Posso aspettare qui.

In Italian, the comma here helps show a pause and connects the second idea to the first: I’m not in a hurry, so I can wait here.

A full stop would also be possible, depending on style and context.

Yes, but it is a little different.

• Non ho fretta = I’m not in a hurry
• Non vado di fretta = I’m not going quickly / I’m not rushing

Avere fretta is the most direct and common way to express the idea in your sentence.
So Non ho fretta, posso aspettare qui is the most natural version for I’m not in a hurry, I can wait here.

You could add emphasis in a few ways, depending on what you want to stress.

Examples:

• Io non ho fretta, posso aspettare qui.
  Emphasizes I
• Non ho fretta, posso aspettare qui tranquillamente.
  Adds the idea of I can wait here спокойно / no problem
• Non ho proprio fretta, posso aspettare qui.
  Means I’m really not in a hurry

The basic sentence is already perfectly natural, but Italian often adds small words like proprio or tranquillamente to make the tone warmer or stronger.