पिता अभी घर आ रहे हैं।

Yes. In Hindi, family relationship words are often used without an explicit possessive when the meaning is obvious from context. So पिता can naturally mean father or my father, depending on the situation.

If you want to be more explicit, you could say मेरे पिता अभी घर आ रहे हैं, but it is not always necessary.

Here, अभी means now, right now, or at the moment.

A useful thing to know is that अभी can also mean just now or soon, depending on context. But in this sentence, with the progressive verb, it most naturally means that the action is happening now.

आ रहे हैं is the present progressive form, so it shows an action that is in progress: the father is currently on the way.

By contrast, आते हैं is usually habitual, meaning something like comes or usually comes.

So:

• पिता घर आते हैं = Father comes home / Father usually comes home.
• पिता घर आ रहे हैं = Father is coming home.

This is because पिता is often treated as an honorific noun. In Hindi, respected singular people often take plural agreement.

So even though it is one person, Hindi uses the more respectful verb form:

• respectful singular: आ रहे हैं
• non-honorific singular masculine: आ रहा है

This is very common with parents, teachers, older people, and other respected figures.

Because पिता is masculine. In the progressive, the participle agrees with gender and number/honorific usage.

So:

• masculine respectful singular: आ रहे हैं
• feminine respectful singular: आ रही हैं

For example:

• माता अभी घर आ रही हैं। = Mother is coming home now.

हैं is the present-tense auxiliary verb, related to to be.

In आ रहे हैं, the full progressive structure is:

• main verb stem: आ
• progressive participle: रहे
• auxiliary: हैं

Together, they form is coming / are coming, depending on context. Here it is used as a respectful singular form, so although the English meaning is singular, Hindi uses हैं.

आना is the dictionary form, or infinitive, meaning to come.

When Hindi builds tense/aspect forms, it usually does not use the full infinitive. Instead, it uses the verb stem plus other elements. Here:

• dictionary form: आना
• stem used in the progressive: आ
• progressive form: आ रहे हैं

So this is completely normal verb formation.

Hindi, like English, chooses between come and go based on point of reference.

आना is used when the movement is toward the place that matters in the conversation. Since the sentence is about reaching home, Hindi often uses घर आना, much like English says come home.

If the speaker were describing movement away from the relevant place, जाना could be used instead.

With motion verbs such as आना and जाना, घर often appears by itself to mean home as a destination.

So:

• घर आना = to come home
• घर जाना = to go home

If you say घर में, that means in the house or into the house, which is a little different.

So घर here works much like English home in come home.

Hindi word order is fairly flexible, although some patterns sound more natural than others.

पिता अभी घर आ रहे हैं is perfectly natural. You may also hear things like:

• पिता घर अभी आ रहे हैं
• अभी पिता घर aa रहे हैं

But the original version is clear and normal. In many cases, अभी is placed before the location or before the verb phrase, depending on what the speaker wants to emphasize.

It most naturally means that the action is in progress: he is on the way home now.

Depending on context, it can sometimes also suggest that arrival is fairly soon, but the basic idea is ongoing movement toward home.

If you wanted to say he has already arrived, you would need a different form, such as पिता अभी घर आ गए हैं.

पिता is correct, but it sounds a bit formal or neutral. In everyday speech, many speakers would more often say:

• पापा
• पिताजी

So all of these can work, but they give slightly different tones:

• पिता = formal/neutral
• पिताजी = respectful and common
• पापा = informal and affectionate

The grammar of the sentence stays essentially the same.

Because this sentence is in the present progressive, not in the perfective past.

In Hindi, ने is commonly used with transitive verbs in certain perfective constructions, but not in a sentence like this one.

So:

• पिता अभी घर आ रहे हैं = no ने
• this is normal because the verb is not in a perfective construction

Also, आना is intransitive, which further helps explain why ने does not appear here.