You and her are listening to each other.

Onun´la dinleşiyorsun.

We are angry with each other.

Birbiri kızışıyoruz

You and him will laugh to each other.

Onun´la gülüşeceksin

They observed each other.

Birbirleriyle gözleştiler

They giving each other a gift.

birbirleriyle hediyeyi verişiyorlar

We hugged each other.

Birbiri sarılışştık

They remembered each other.

Birbirleriyle hatırlaştılar.

I can´t understand, uhhmm..when should I use the suffix -iş ?

 Is it used to make some verbs into some nouns?

Like çıkmak = to exit ---> çık+ış - çıkış = exit, and uçmak - to fly ---> uç+uş - uçuş = flight. etc.

I´m not sure if I´m right, but that´s my understanding on it, can anyone explain more, please?

The -iş form of verbs

When you see -iş or one of its variants after the stem of a verb, it means each other.

Yarın görüşürüz.= We´ll see each other tomorrow.

Bakışıp aşık oldular.= They looked at each other and fell inlove.

Öpüştünüz mü?= Did you kiss (each other) ?

We don´t use "-iş" (together) for every verb in Turkish.

dinlemek does not receive "-iş"

You and her are listening to eacher:

Birbirinizi dinliyorsunuz.

Kızışma is used for a different meaning: it is generally used in meaning of "to become hot"

For saying "we are angry at each other" :

Birbirimize kızgınız.

Gözleşmek is incorrect. "to observe" is "gözlemlemek/gözlemek"

They observed each other:

Birbirlerini gözlemlediler/gözlediler.

Verişmek doesn´t mean "to give something to each other"

Vermek veriştirmek is an expression, to have a rough tongue.

They are giving each other a gift:

Birbirlerine hediye veriyorlar.

Sarılışmak is correct, it means "to hug each other"

Hatırlaşmak is incorrect:

They remembered each other:

Birbirlerini hatırladılar.

thx

turkishcobra

  Sometimes the -iş form has a meaning beyond just each other:

sevmek= to love

sevişmek= to make love

bulmak= to find  

buluşmak= to meet

anlamak= to understand  

anlaşmak= to agree

tanımak= to recognize, to be aquired with            

 tanişmak= to become aquired, to meet for the first time

gelmek= to come

gelişmek= to develope

ex.

Birbirimizi seviyoruz. = We love each other.

Sevişiyoruz. = We are making love.

There are two things wrong in your post.

We don´t use "-iş" (together) for every verb in Turkish.

We can add the suffix -iş (-ış,-uş,-üş to all the stems and the roots of the Turkish verbs.It is one of the most widely used three constructive suffixes (the others are -mak, -mek and -ma, -me) that are used to make nouns from verbs. -ış, -iş, -uş, -üş  more or less has the same function as the suffix -ma,-me, but it is more suitable to make object names: at-ış, bul-uş, bak-ış, anla-y-ış, göster-iş, doğ-uş, gül-üş, dur-uş, yürü-y-üş, etc.

dinlemek does not receive "-iş"

No Turkish word ending in the suffix -mak,-mek takes the suffix -iş. But the main thing that you can´t see is that dinlemek is a noun, but not a verb. The verb stem is dinle-, and it can take the sufix -iş: dinle-y-iş. 

Coming to keren´s question:

I can´t understand,uhhmm..when should I use the suffix -iş ?

Only those which can also be suffixed by -mak, -mek, can be used as verb stem. For example, at-ış-mak, bul-uş-mak, bak-ış-mak, gül-üş-mek,etc. But those that can never be suffixed by -mak,-mek, can never be used as verb stem.For example, anla-y-ış, göster-iş, yürü-y-üş, etc. To know that you can use your dictionary.For this, the first thing you have to do is to find the verb stem.Let our example be the following:

gül- (verb stem)

gülüş (noun formed by adding -üş

gülüşmek (noun formed by adding the combination of -üş + mek)

Now see if your dictionary has the word gülüşmek.

If it has, you can use gülüş- as verb stemthis means you can add to it any proper inflectional suffix)

gülüş-tü-nüz, gülüş-tü-ler,etc.  

You should keep in mind that adding -mak,-mek to a word which is already suffixed by -ış,-iş,-uş,-üş may sometimes make the meaning completely different (especially with the ones that are object names):

al- (receive, buy, take)

al-ış (receiving, buying, taking)

al-ış-mak (to get used)

gel- (come)

gel-iş (coming, arriving)

gel-iş-mek (to develop, grow up)

If one of your examples would be "we looked at each other", then you could also translate it in Turkish as "bakıştık".

Apart from sarılış-, you were unlucky in choosing the verbs. Next time you will do it better inşallah.