Is there a language, in which the word for "coffee" does not contain the sounds k/q and f/h/v, i.e. the word has a different root?
First of all I would like to say that these words are not cognates; they are loanwords.
The coffee plant is indigenous in the highlands of Ethiopia. It was transplanted to the Yemen in the 14th century (which is fairly recent), where the drink coffee became popular among Sufi circles, and was soon after exported to Istanbul, and hence to Europe. For a long time coffee was produced only in the Yemen and the Horn of Africa.
The “coffee” word comes from Arabic qahwa, originally the name for a sort of wine, but which the Yemeni coffee-drinkers transferred to their favourite tipple. It has been claimed, but never proved, that it has antecedents in one or the other of the languages of Ethiopia, but until proven otherwise, it is more likely that the Ethiopian names are borrowed from Arabic. Arabic qahwa was borrowed into Turkish as kahve, and from Turkish to Dutch koffie, French café etc.
The native Ethiopian word for “coffee” (the plant and the drink) is būn. In most Arabic dialects bunn is the berry and qahwa is the drink, but in the Yemen bunn is used both for the berry and the drink. The Dutch traders identified, by folk-etymology, Arabic bunn with Dutch boon “bean”, and it is for this reason that in English too we wrongly refer to “coffee beans”. Coffee is not made from beans but from the dried seeds of coffee berries.
There are languages that have invented new words for "coffee", but in virtually all languages in the world the principal word for coffee derives from one or the other of the mentioned Arabic words.
Here is an excellent scholarly discussion of the whole complex:
- Armenian: սուրճ
- English: java (Wiktionary)
In the 17th century, the Dutch colonized the island of Java, which is now part of Indonesia. They planted lots of coffee there and began exporting it to the rest of the world. It was successful enough to have become a generic word for coffee. — Quora
the word for "coffee"
does not contain the sounds k/q and f/h/v
In Navajo, the word for "coffee" doesn't contain k/q: ahwééh. Yet, it looks like a loanword.
the word has a different root
In Oromo it is called buna and very likely has a different root. But I don't know if it's the only word for "coffee" in this language.
Edit: take a look at this Reddit thread, there are quite a few more languages mentioned there: Amharic, Ojibwe, Cheyenne, Tibetan, South Sami, Kichwa, Lakota...
The Oxford English Dictionary indexes a number of slang terms for 'coffee'. Two of them are clearly derived from coffee, so I'd consider them scratched for your purposes — Everton toffee (rhyming slang), joe (alliterative slang). But there are five others that probably pass muster: Java, mud, ninny-broth, syrup of soot, Turkey gruel.