glides in Latin with the letter i

The initial i works as a consonant, like our y in yule or yelp. So the Iu- of Iulius or Iulia is just one syllable; the u is long (just as in our Julius).

Similarly with e.g. iudex, ianua, iam.

I am glad I am teaching this correctly - I had a new latin student today and this is what I told her!

What’s hidden, except in texts which use quantity marks, is the quantity of the vowel that follows the i: long u in Iulia, long a in ianua, short a in iam.
Older texts used j for this consonantal i, convenient but wrong.
As to initial ie, ia, and io, yes the i is consonantal except in a few words (mostly Greek names) where it’s a regular vowel. You won’t find iy, since y is not a Latin letter.

I’d like to go further in that direction.

We do have iam (jam) on one side, but on the other side, we have etiam, which looks like it’s in three syllables while it comes from et-jam, and so we should expect etjam. Can someone clarify that?

The same problem arises with u/v. For example, I read suāvis was in fact pronounced svāvis. How can we tell in such situations whether we have v or u if it’s not in the spelling? Shouldn’t the spelling be changed in order to be more consistent with pronunciation?

No, Iulius is three syllables, like our Julius. Note I said the initial i works like a consonant. -ius in the ending is two syllables, since there the i is a regular short vowel.
Similarly Aemilia has four syllables (Ae-mi-li-a).

As to accent, in classical times Aemilia would have been accented on the antepenult (-MI-), just like Iulius (IU-). With -que tacked on to the end of it the accent probably stayed the same, with perhaps a secondary accent on the syllable preceding the -que.

As to Aurelianus’ problems, he knows that the i in iam was consonantal, just as it presumably was in etiam too. And suauis is disyllabic—it makes no difference whether we use u or v for the medial consonant. (Accepted practice these days, despite the risk of occasional confusion, is to use u regardless of whether it’s functioning as a consonant or as a vowel; and the same goes for i.)

Verse often helps, and it’s not hard to learn to read hexameters. All it takes is a little practice.
Virgil has “Idaeumqu(e) etiam currus, eti(am) arma tenentem”
and Lucretius has “hoc ubi quod suau(e) est aliis, aliis fit amarum.”