So with this, is it a mistake or do sentences need to be capitalized at the start?
Sentences have to start with a capital letter, but this isn't a sentence. It's just a phrase without a predicate.
No difference in meaning -- you just use az before a vowel and a before a consonant.
(In this respect, they're similar to "a" and "an" in English -- we say "a horse" and "an elephant" not for any grammatical reason, but just because the choice between the words is governed by sound.)