A consonant sound means a sound in the left column in the table linked below. For the purpose of the “no three consonants” rule, you should not count a semivowel as a consonant.
Note that this is in terms of IPA and not the written language, where, as in English although not quite as bad, there are a number of words that are spelled illogically that you just have to memorize how to pronounced. However, in terms of writing, the definition of “consonant” is usually the same as what you learn in school for English — everything but a, e, i, o, u, y. Bear in mind that nasal vowels are in no way consonants, even though an n is written.
Schwa deletion is extraordinarily difficult and intricate, and I have found that when you ask native speakers, the way that they actually talk and the way that they think they talk differs enormously (je m’excuse mais c’est la vérité). For a complete guide you might try the book The Sounds of French by Tranel, which I like a lot, but be warned that it’s way more detail than you want to get into when you’re first starting out.
Finally, although this is not correct, the good news is that you can always pronounce a schwa if you feel like it, with little impediment to understanding. In classical French poetry and music, all schwas are pronounced. In pop music, schwas are pronounced sometimes and not other times, basically if the singer needs something to fill an extra beat. A lot of French speakers will, to pause to think, enunciate an otherwise unpronounced schwa. When French people are saying a word slowly to make sure you understand it, they very often pronounce schwas that are otherwise not pronounced, even the silent “e” at the end of the word which is never pronounced.