So, translating again, and I've run into something else the various dictionaries I have access to are unable to provide a definition for, clearly the word in my title. I've been able to find a few words that end in 変わらず, such as 相変わらず. Judging from the meaning of the base character, I'd think that 変わらず probably means the opposite of 相変わらず--changing or inconstant, leading me to believe that, in the context it's in (いつも変わらず), a translation along the lines of "ever-changing" would be appropriate. But this is just going on instinct, so... help?
One of the things you should rethink is about 'aikawarazu' being more of a phrase or expression rather than a normal word.
Then, 'kawarazu' is just the -zu form of 'kawaru'. Usually it's interchangeable with the negative form, but with a 'ni' at the end it's sometimes negative -te.
According to Gjiten 相変わらず transleates to: as ever; as usual; the same;
i agree with what AzureDark said about it being easier to understand 相変わらず as a phrase. it means, as Aizmov has pointed out, "as ever; as usual; the same;"
an example sentence:
(my grandad is healthy as usual/always)
変わらず on the other hand is just the more formal version of 変わらないで.
verb + て has many functions like requests, joining sentences etc. but in this situation it means "to have this action happening whilst something else happens". maybe what i just said is difficult to understand (im not sure even if I understand what i just said myself lol) so let me give u some examples:
i walked with my umbrella opened (or more natural english: i opened my umbrella and walked)
she came with make up on
in the same way u can also have this is in the negative form i.e. verb + ないで or the more formal version verb + ずに. it means "without something happening, something else happens). if u use it before a pause in the sentence, u can throw the に away so it becomes just verb + ず.
without any change in its functions, the ipod has become thinner and lighter
this week also without change, Kobukuro is number 1 on the Oricon chart (or more natural english: Kobukuro is no.1 again on this week's Oricon chart)
I've actually never heard of a -zu ending; so it's a more formal verb ending than ないで, but is it more formal or less so than... actually, I can't recall offhand what the -te ending form for ません would be; in any case, how does it compare (in formality) to the ます construction?
u cant compare verb+ず with verb+ません. theyre 2 different pieces of grammar with 2 different uses and 2 different meanings.