The word is almost certain to be borrowed from German through Polish (though, a very long time ago).
"Smaka" is also the Swedish word for the verb "to taste." I'll bet that the Ukrainian word came from the Swedish, since Vikings settled in Kyiv over a thousand years ago.
The word "smak" comes from Polish which has had quite intensive contacts with German language. The later similarity is rather incidental. There are very few borrowings known definitely from Vikings (there should be a little more in Russian from Novgorod/North).
That depends on the history of the Swedish "smak". I'd say the chance of such an origin to be true is rather slim. Words that were borrowed that long ago typically look nothing alike. The similarity suggests the borrowing being quite recent (or Swedish and Ukranian being extremely lucky to closely follow each other's phonetic changes for a millenium).
In dutch, 'smaak' is (a) taste and 'smaken' to taste (mostly when its tasty)
Actually this word came from germanic tribe of goths, who lived on the modern polish and ukrainian territory.
How can you tell the difference between "this food is very tasty" and "this very tasty food"?
"Це [є] дуже смачна їжа" = This is very tasty food ("This" is the subject of the sentence)
"Ця їжа [є] дуже смачна" = This food is very tasty ("This food" is the subject of the sentences)
"Ця дуже смачна їжа" = This very tasty food (not a sentence)
Note: є is skipped leaving only a trace. This is why it's so tough for foreigners to differentiate these two sentences, because they have only an invisible trace of "to be" :)
How do you know it is смачна instead of смачні? Is it the gender of їжа?
No: "смачна" - singular feminine, "смачні" - plural (feminine+masculine+neuter), смачний - singular masculine.
I'm trying to ask "Can I have a taste?" of the very delicious food. And it looks like I forgot to conjugate Мати. Fixed it, but I'm not sure if my edit is correct.
Oh, I think I understood. You can't say that in Ukrainian. We have a verb for that: куштувати or пробувати (try).
Чи можу я скуштувати? Можна спробувати?