मेरे फोन में माँ की एक पुरानी तस्वीर है, और आपके फोन में मेरी बहन की नई तस्वीर है।

Hindi very often expresses have with a location/existence pattern rather than a direct verb like English have.

So:

• मेरे phone में ... तस्वीर है literally means In my phone, there is a picture...
• In natural English, that often becomes My phone has a picture...

This is a very common Hindi structure. You will see the same idea elsewhere too:

• मेरे पास किताब है = I have a book
• कमरे में कुर्सी है = There is a chair in the room
• फोन में तस्वीर है = There is a picture in the phone

So the sentence is perfectly normal Hindi, even though it feels more like there is than have.

Because फोन is followed by the postposition में, so फोन is in the oblique form. When a masculine singular noun goes into the oblique before a postposition, words that agree with it also change.

Compare:

• मेरा फोन = my phone
• मेरे फोन में = in my phone

Here:

• मेरा is the direct form
• मेरे is the masculine oblique form

This is one of the most important patterns in Hindi grammar.

For the same reason as मेरे फोन में.

• आपका फोन = your phone
• आपके फोन में = in your phone

Since फोन is before the postposition में, it is oblique, so आपका changes to आपके.

Also note that आप is the polite/formal you, so आपके here means your in a polite or respectful way.

Yes. In Hindi, if something is stored inside a device, में is very natural.

So:

• फोन में तस्वीर है = there is a picture in the phone

For digital contents, Hindi often treats the phone as a container.

By contrast, फोन पर usually suggests something more like:

• on the phone screen
• on the phone as a device
• via phone / by phone

So in this sentence, में is the best choice for a stored picture.

This is the genitive pattern, similar to of or the English apostrophe 's.

• माँ की तस्वीर = mother’s picture / a picture of mother

The marker का / की / के agrees with the noun that comes after it, not with the possessor.

Here the noun after it is तस्वीर, which is feminine, so Hindi uses की:

• माँ की तस्वीर
• not माँ का तस्वीर

If the possessed noun were masculine, it would change:

• माँ का फोन = mother’s phone

Because there are two layers of relationship:

1. मेरी बहन = my sister
   Here मेरी agrees with बहन, which is feminine.

2. बहन की तस्वीर = sister’s picture / picture of the sister
   Here की agrees with तस्वीर, which is feminine.

So the whole phrase works like this:

• मेरी बहन = my sister
• मेरी बहन की तस्वीर = a picture of my sister

This is a very common nested structure in Hindi.

Because they describe तस्वीर, and तस्वीर is feminine.

So Hindi makes the adjectives agree with तस्वीर:

• पुरानी तस्वीर = old picture
• नई तस्वीर = new picture

If the noun were masculine, the adjective form would usually be masculine instead:

• नया फोन = new phone
• पुराना फोन = old phone

This agreement is very normal in Hindi.

एक literally means one, but it often works a lot like a/an in English.

So:

• माँ की एक पुरानी तस्वीर = an old picture of mother

It is not always strictly required, but it sounds natural and helps introduce a singular countable noun.

You could also say:

• मेरे फोन में माँ की पुरानी तस्वीर है

That is possible, but एक makes it sound more like there is an old picture rather than referring to some already known picture.

Because in each clause, the thing that exists is singular:

• एक पुरानी तस्वीर है
• नई तस्वीर है

Since तस्वीर is singular in both parts, Hindi uses है.

If the noun were plural, you would use हैं:

• मेरे फोन में माँ की पुरानी तस्वीरें हैं = There are old pictures of mother in my phone.

Yes, फोन is normally treated as a masculine noun.

That is why you get forms like:

• मेरा फोन
• मेरे फोन में
• आपका फोन
• आपके फोन में

Many borrowed nouns in Hindi simply have a grammatical gender by usage, and फोन is commonly masculine.

Hindi word order is flexible, though some orders sound more neutral than others.

The sentence as given is very natural and neutral:

• मेरे फोन में माँ की एक पुरानी तस्वीर है

But you could also say:

• माँ की एक पुरानी तस्वीर मेरे फोन में है

That version puts more attention on the picture first, then says where it is.

So the original sentence is not the only possible order, but it is a very standard one.

Because आप is the polite/respectful form of you.

So:

• आपके फोन में = in your phone, polite/formal
• तुम्हारे फोन में = in your phone, familiar/informal

The grammar pattern is the same, but the level of politeness changes.

Usually it means an old photo in the natural everyday sense: a photo from long ago, or an old existing picture.

In practice, English and Hindi behave similarly here. The adjective पुरानी is attached to तस्वीर, so it describes the picture, not माँ.

Likewise:

• नई तस्वीर = a new picture / a recent picture

So the sentence contrasts:

• माँ की एक पुरानी तस्वीर
• मेरी बहन की नई तस्वीर

That contrast is between old picture and new picture, not between old mother and new sister.

Yes, absolutely.

• मेरी बहन की नई तस्वीर है
• मेरी बहन की एक नई तस्वीर है

Both are grammatical.

Adding एक makes it more explicitly a new picture. Leaving it out can sound slightly more general or slightly less focused on counting.

So the original sentence is fine, and एक could be added there if the speaker wanted that nuance more clearly.