Min søsters mobil ligger på bordet i stuen.

Because Danish uses -s to mark the genitive, just like English uses apostrophe-s.

• søster = sister
• søsters = sister’s

So:

• min søster = my sister
• min søsters mobil = my sister’s phone

Danish does not use an apostrophe here. It is just søsters, not søster’s.

Here min belongs to søster:

• en søster = a sister

Because søster is a common-gender noun (en-word), the possessive is min.

Compare:

• min søster = my sister
• mit barn = my child

So min søsters mobil literally starts with my sister’s.

Because after a possessive, Danish normally uses the noun without the definite ending.

So:

• min mobil = my phone
• Peters bil = Peter’s car
• min søsters mobil = my sister’s phone

Just like English says my sister’s phone, not my sister’s the phone, Danish does not add the definite ending here.

In Danish, the is often added to the end of the noun.

• et bord = a table

• bordet = the table

• en stue = a living room
• stuen = the living room

So:

• på bordet = on the table
• i stuen = in the living room

This is one of the biggest differences from English: Danish often puts definiteness on the noun itself instead of using a separate word.

Danish often prefers a position verb when describing where something is.

• ligger = lies / is lying
• står = stands / is standing
• sidder = sits / is situated
• hænger = hangs

A phone on a table is usually thought of as lying, so ligger sounds natural:

• Min søsters mobil ligger på bordet = My sister’s phone is lying on the table

You can sometimes use er for location, but ligger is more idiomatic here.

Because the two prepositions describe different kinds of location.

• på = on
• i = in

So:

• på bordet = on the table
• i stuen = in the living room

A table is treated as a surface, so Danish uses på.
A living room is treated as an enclosed space/room, so Danish uses i.

Yes. In Danish, mobil is a very common short form of mobiltelefon.

So mobil means:

• mobile phone in British English
• cell phone in American English

In everyday Danish, mobil is completely normal and very common.

The sentence follows normal Danish main-clause word order:

• Min søsters mobil = subject
• ligger = finite verb
• på bordet i stuen = location

So the pattern is basically:

• Subject + verb + rest

Danish main clauses normally put the finite verb in the second position. That is an important rule in Danish.

This sentence could also be rearranged for emphasis:

• På bordet i stuen ligger min søsters mobil.

That still means the same thing, but now the location comes first, and the verb ligger still stays in second position.