I´m asking about sentences like

I saw Ali´s grandmother, sisters, cousins and cat.

where there are several equivalent nouns listed and connected together with and. I have noticed that in Turkish the numerous endings are saved so that only the last one is case-marked.  I guess the possessive and plural endings are shown in every word, anyway.

How is the rule exactly?

we use and before the last word linked the group

for example

Ben Türkçe , İngilizce  , İspanyolca ve Arapça biliyorum.

But suppose the listed nouns demand possessive, plural, case and whatever endings there are. Are they all repeated in every noun?

And besides, what is the difference between ve and ile?

 Literally ve means and and ile means with

So we might say

İngilizce ve Türkçe biliyorum. I know English and Turkish

Ali ile Gülten sinemaya gitti. Ali went to the cinema with Gülten

or you could say

Ali ve Gülten sinemaya gittiler. Ali and Gülten went to the cinema (here it is "they" went, not "he went with" so -ler)

It also works like this when the things in the list are verbs 

e.g.

Ali ve Ayşe, yatmadan önce dizi seyredecek, mektup yazacak ve küzenlerine telefon edeceklerdi.

Ali and Ayşe were going to watch a TV show, write a letter and call their cousins before going to bed.

The -lerdi ending we only need to put on the last verb in the list. All of the other verbs take the same ending by implication.

Thanks, MarioninTurkey. So, tense and person are only visible in the last verb of the list.

Interesting assumption,but it is not correct.

geldim, gördüm,yendim (veni,vidi,vici)

-di (past tense)-m(1st person singular)

Let´s change the subject to 3rd person plural:

geldiler, gördüler,yendiler.

But if you use a tense which consists of two suffixes (as in marionin´s example) you don´t have to use either one with each verb. Let´s make the subject 3rd person singular and the tense -ecekti (=would):

gelecek, görecek,yenecek.ti

As you know 3rd person singular has no personal ending.

Let´s now make the subject 3rd person plural:

gelecek, görecek,yenecek.ti.ler / yenecek.ler.di .

In this type of sentences PE is used only with the last verb.

another example (-miş-ti):

gelmiş, görmüş, yenmiş.ti.m

yet another example (-cek-miş:

gelecek, görecek, yenecek.miş.sin

I am not an expert but a native speaker of the language and maybe our "masters" will help you more

Scalpel, good you noticed. It seems that I generalized a very special case where two tense marks were in the same word.

Master or not but you made it clear. (Besides, I´m afraid all the masters are fed up with my endless questions.) Sağ olun.

"ile" also gives "ve" (and) meaning sometimes.

Ali ile Gülten sinemaya gitti. Ali and Gülten went to the cinema.

Tense should always be added (with some exceptions) but personal suffix may be omitted sometimes:

Gelir, gider-im = gelip gider-im  = gelir-im, gider-im

Gelir, gider-di-m = gelip gider-di-m  = gelir-di-m, gider-di-m

Neler neler görecek , duyacak-sın = neler neler görüp duyacak-sın = neler neler görecek-sin, duyacak-sın

etc.