Others have already covered most of the issue.

1. We can omit personal adjectives whenever it is clear from the possessive suffix to whom the word refers to. This doesnt mean it is always alright to omit the personal adjectives. Indeed sometimes it is not a good idea.

In your example we have two issues. The first issue is that the plural suffix -ler is going to get mixed with the third person possessive suffix -ler. Actually this confusion is avoidable since in modern Turkish the third person plural suffix is replaced with the singular suffix. So we normall prefer "onların evi" instead "onların evleri" for a single house.

I have updated my list of possessive suffixes. If you stick to that list you will be always on the right side.

The second problem rises when we omit the personal adjectives. The workaround I found for this problem is not to omit the personal adjectives in three cases as shown below.

Possessive Suffixes

after a consonant
my – benim -ım -im -um -üm
your – senin -ın -in -un -ün
his/her/its – onun -ı -i -u -ü
our – bizim -ımız -imiz -umuz -ümüz
your – sizin -ınız -iniz -unuz -ünüz
their – onların -ı -i -u -ü

after a vowel
my – benim -m
your – senin -n
his/her/its – onun -sı -si –su -sü
our – bizim -mız- miz -muz -müz
your – sizin -nız -niz -nuz -nüz
their – onların -sı -si –su -sü

single object

benim kedim
senin kedin
onun kedisi
bizim kedimiz
sizin kediniz
onların kedisi

kedim
kedin
kedisi
kedimiz
kediniz
onların kedisi

multiple object

benim kedilerim
senin kedilerin
onun kedileri
bizim kedilerimiz
sizin kedileriniz
onların kedileri

kedlerim
kedilerin
onun kedileri
kedilerimiz
kedileriniz
onların kedileri

2. This is called a noun modification:

Otobüs durağı : Bus stop

This is an undefined noun modification because the first noun isn't defined but only the second is. It is not a certain bus that we are talking about.
In noun modifications if it is a defined one the first noun takes suffixes as well.
If the first noun takes suffixes it takes one of these:
-ın -in -un -ün , -nın -nin -nun -nün
The modified noun always takes a suffix which is one of these:
-ı -i -u -ü , -sı -si –su -sü


Otobüsün kapısı : the door of the bus

This is a defined noun modification. As you see this time both nouns have taken suffixes.

Ali'nin arabası : Al's car
Again a defined noun modification.

"Annem" means my mother. To say "my mother's name" we need to make a defined noun modification since it is defined.
So, "my mother" is "annem" and "name" is "ad" which both take noun modification suffixes as shown above. And it becomes:

Annemin adı : My mother's name

Annem+in ad+ı : If you don't understand why we have used -in and -ı here I can explain the vowel and consonant harmony rules.

3.