Well, technically yes, but this is likely to be written with a dash: «Привіт — друг». Also, you might add «це»: «Приві́т — це друг». It also would be pronounced with a different intonation.
If you want to make sure your direct address is not mistaken for anything else, you could use the vocative case form: «Привіт, друже!» 'Hello, friend'. Many Ukrainians like this form. :)
Yes, you're right, і is a closer vowel than и, so it has a softer sound. Also, і makes the preceding consonant softer (e.g. в in привіт is semi-palatised, while in ви it's not palatised).
І is transribed [i], while и is transcribed [ɪ]. This is similar to sheep-ship difference in English, although it doesn't affect the vowel length, only the vowel quality.