Russian (and other Slavic languages that use the Cyrillic alphabet) contain the letters Ю and Я, which have unusual (from a Westerner’s perspective) sound values. Ю is yu, and Я is ya.
How are these letters thought of in the languages that use them? Are they vowels or consonants? Do they count as a syllable for the purposes of the syllabic count of a word?
It’s been a while since I studied Russian, but I think this is the gist of it:
Vowels come in pairs, for example A and Я. “A” represents the pure vowel sound, as in English ‘father’. If Я is at the beginning of a word, it represents a y-glide plus the vowel sound. Basically ‘ya’ as in the OP.
It’s a little different if the vowel follows a consonant. Russian consonants mostly have two versions of each sound, a standard sound and the same sound made with the tongue pushed up to the roof of the mouth, called palatization. ‘A’ is used before a standard consonant, Я is used to indicate that the consonant is palatized.
Exactly my memory from 50 years ago!
I posted before I had finished. An example is the word for yes, ДA, prounced like ‘da’, compared with ДЯДЯ, uncle pronounced like ‘djadja’.
These letters are considered vowels.
How these vowels effect syllable count is a bit above my level of expertise. 
Not a native speaker, but I’m pretty certain those letter would be considered гласные (vowels - @terentii ?). Remember, though, that phonologically, letters are representations of sounds, and not the sounds themselves. So, pedantically, no letter (Roman, Cyrillic, or whatever) is a “consonant” or “vowel”. But I realize they are categorized that way casually in non-academic contexts.
Do they count as a syllable for the purposes of the syllabic count of a word?
Almost invariably, syllables containing Ю or Я would be separate syllables.
I believe they’re called “jotated” vowels. In other words, “a” and “u” preceded by the “y” (or “j”) sound. This has the effect of “softening” the latter two, in effect combining the hard vowels with “soft signs” (myagkiye znaky).
For example:
With a word like bukva (“letter”), which ends in a hard vowel, you drop the “a” in the genitive plural: Pyat’ bukv = “Five letters.” (Any number above four automatically takes the genitive plural.)
With a word like Anya (the female name), which ends in a soft vowel, you drop the “a” but retain the soft sign. “The five Anyas” thus becomes Pyat’ An’," the apostrophe in this case representing the myagkiy znak.
Russian grammar may seem confusing to someone who hasn’t tried learning the language, but it isn’t really. There are a lot of rules, but they’re all fairly regular, in contrast to Polish and Czech (and German and Latin, for that matter), which are very arbitrary.
In Cyrillic: “The five Anyas” = Пять Ань. The last letter is the soft sign.
I can beat that, I studied Russian in high school in 1965 through 1967, and one term in college in '68-'69 (I think it was winter term). Hated my university’s style of teaching language, so I only took one term.
One more point on the “Я” – English writers tend to think of it as a backwards “R”, but it’s better to think of it as an elevated “a” in cursive writing. The enclosed part of the “a” rises up higher. I’ve long wondered if it has some evolution from the cursive shape of the “a” in so many languages.
I had Russian classes at the Anglo-American School of Moscow in 1977. My teacher was Russian. She had been a teacher of Russian in the public schools in Moscow, retired, and then took this gig at the AASM teaching a few days a week for a few hours. Many of our teachers were retired public school teachers, and a few others were university students working on the equivalent of PhDs. All the Russian teachers were native speakers.
We barely touched on consonants and vowels. It was unusual to me, because my English books in the US seemed obsessed with categorizing sounds as consonants or vowels.
But what is important about Ю & Я (as well as Е, Ё & И) is that they soften the previous consonant. They kind of have a built-in ь. They are called “soft” vowels, therefore. The other vowels are “hard” vowels, etc.
What you are hearing as a “semi-consonant” sound is just the influence of the vowel over the previous consonant.
Since I was taught Russian by a teacher of Russian who happened to speak English (and really, not all that well-- I was in the advanced class, and it was taught in Russian), and who was hired mainly for her experience with children, not in teaching Russian as a second language, I was taught Russian more as a first language. Albeit, I was taught as it would be taught to a child a few years younger than I was. So, these grammar points were not “translated” for me. Some of them, like this one, came to me in “aha” moments years later-- that is, I made the connection to a point in English many years later.
Anyway, I guess the answer to “What they are,” is “soft vowels.” That may not be very satisfying, because there is not equivalent in English, but that is the best answer I have.
Я did indeed evolve from a cursive form, but of a different letter once called a “yus”. Specifically, a “little yus”:
Dayum. Ignorance fought, or what?! Only on the Dope!
A friend of mine used to refer to the stores as “Toys Ya Us”.
Your friend was not the only one.