I'm very new to Church Slavonic. It's like some of the texts we read from has only modern Russian letters and other texts have the Slavonic that writing that was used in churches before 1917.
It's not surprising. Very often (among all Slavs) the choir's parts are written in "modern" letters (Russian, Serbian, in Poland sometimes even not in Cyrillic, but in latin letters) and all the rest (so mainly priests' and readers' parts) in Church Slavonic letters, as usually musical notation goes along with modern letters.
In the Divine Liturgy, do they normally sing EVERY Kondakia and Troparia on those lists or do they pick just a few out of the list?
Haha, absolutely not, unless it's monastery or seminary (but even then not always; just imagine, if we commemorate sometimes 20 saints on one day, it would last definitely too long, especially that not every parish has hymnographic materials for many saints).
In Does it matter what specific order they're sung in?
1st is always the troparion of the feast that's from the 12 greatest ones (ofc if it's festal period of one of them), unless it's Sunday and it's not the 1st day of the feast, so it's 1st Sunday troparion and then to the feast. After festal/Sunday and then festal troparion if there is a commemoration of a great saint(s), the troparion for them is chanted. After it should be chanted troparion of the temple you're praying in, and then kontakion(s). For more precise rule you have to know typikon, but the vast majority of laypeople don't have idea about it (someitems, unfortunately, choir directors and priests including), so don't worry too much