я просто дивлюся is not used by Ukrainians when approached by shop assistants. It is a fictitious expression is just a translation of the English phrase.
Is there another way they say something similar or does this situation not occur in Ukraine for the most part?
If approached by a shop assistant in this kind of a situation, I would say "Я поки що тільки дивлюся" (I'm only looking so far) or "Я ще не вибрала" (I haven't chosen [anything] yet) or a couple of other ways to convey the message :)
Note: Я просто дивлюся has a much wider spectrum of meanings than just telling shop assistants off.
Most usually they ask in stores if they could help you and you answer "ні, дякую". Saying "я просто дивлюся" for that sounds a bit unnatural and rude. But one may use the phrase under some circumstances. And of course there are other cliches in such situations.
Well, "дивився" is the past tense for a masculine person in singular, here (because of "я") for the first one.
It is grammatically 100% correct, but since it is in past tense, its meaning changes. Now it would be traslated to "I just watched".
In "type what you hear" I am noticing that the sounds are misleading. When "и" is required in the word it is sounding like "е". It is not just this question but has occurred in others as well.