Learn Hardcore Turkish: Kanepe minderlerini çıkarıp temizleyelim. - Let’s take off the sofa cushions and clean them.

The suffix -ıp is one of Turkish’s converb (short adverbial clause) endings. It attaches to the verb stem çıkar- (“remove/take off”) to link two actions by the same subject. Çıkarıp literally means “removing (them) and then…” or “after removing (them),…” and allows you to connect that action directly to what follows.

Why isn’t the suggestion suffix -elim attached to çıkar as well?

When verbs are chained with the -ıp converb, only the final verb carries the tense or mood marking. Here the hortative (suggestion) suffix -elim appears on temizle- only, giving temizleyelim “let’s clean.” So çıkarıp temizleyelim means “let’s remove (them) and clean.”

How do the suffixes -ler and -ni work in minderlerini?

-ler is the plural marker on minder (“cushion”), forming minderler (“cushions”).
-ni is the accusative case suffix (-i) plus a buffer n (because minderler ends in a vowel). This marks the noun as a definite, specific direct object: “the cushions.”

Why is the accusative suffix used on minderlerini? Can it be omitted?

In Turkish, you add the accusative suffix when the object is definite or known. Here minderlerini refers to the specific cushions of the couch, so it gets -ni. Omitting it (minderleri) would sound more indefinite or general (“let’s remove cushions” rather than “let’s remove the cushions”).

What does the suffix -elim in temizleyelim express, and who is the subject?

The suffix -elim is the 1st person plural hortative ending (“let’s”). It expresses a suggestion including the speaker and others. Temizleyelim means “let’s clean,” with the “we” subject implied by the verb ending.

Could you use çıkaralım instead of çıkarıp? How would that change the sentence?

Yes. You could put the hortative on both verbs:
Kanepe minderlerini çıkaralım, sonra temizleyelim.
This means “let’s remove the couch cushions, then let’s clean them.” The -ıp converb version (çıkarıp temizleyelim) is simply more concise for two linked actions.

How would you tell someone else (not including yourself) to remove and clean the cushions?

You’d use the 2nd person plural/polite imperative:
Kanepe minderlerinizi çıkarın ve temizleyin.
Here:

çıkarın = “remove” (you, plural or polite)
temizleyin = “clean” (you, plural or polite)
minderlerinizi uses -iniz as the 2nd person plural/polite possessive.

Can we omit kanepe and just say minderlerini çıkarıp temizleyelim?

Yes—if it’s clear from context which cushions you mean. Omitting kanepe gives “let’s take the cushions off and clean,” but adding kanepe specifies “the couch cushions.”