Take a C major scale in the bass: how would this best be harmonised if there was no melody to follow? Theorists of the 18th century were quite consistent in this, the so-called Rule of the Octave, but they sometimes disagreed on how to treat the 2nd scale degree, the D. It invariably required a 3rd (F) and a 6th (B) above the bass (Example 1 abov), but sometimes (especially later in the century), the 4th (G) was added, resulting in what modern theorists consider a dominant 7th in 2nd inversion (V4/3, Example 2 below).
But what about the many cases (in theory and in music) where the 4th was omitted? In Roman-numeral analysis, this chord would usually be labelled vii°6, but often considered a dominant 7th in 2nd inversion with the root (G) missing. The problem with this view becomes clear when considering standard 18th-century voice-leading principles. One of these is that the 7th should always resolve downwards, as it indeed does in Example 2, but not in Example 1.
If you thought Example 1 was just plain wrong: well, it's taken from a treatise by Johann Philip Kirnberger, who had been a pupil of none other than Johann Sebastian Bach. Kirnberger sees the origin of this chord in the 7th-chord but struggles to explain why the F often rises, saying merely that the last chord would otherwise lack the G.
The other 'rule' that is often broken is that the 7th (if one understands it as such here) must not be doubled. There are plenty such examples in Bach's chorales, but Example 3 (below) is taken from another important treatise by Johann David Heinichen, which demonstrates that either the bass note (D) or the 3rd above it (F) can be doubled, just not the 6th (B), which, as Bach himself wrote in his thoroughbass rules, would 'sound bad' (see Example 4 below). The reason for this is that the 6th is the leading note, which is generally not doubled in any chord with a dominant function.
By now it should have become clear that I would answer both questions in the title with a ‘no’. First, theorists at the time followed practices outlined by composers, doing their best to explain why chords were used in certain ways. There was also hardly any distinction between them: some composers wrote treatises, and theorists generally also composed. Heinichen was actually a rather eminent composer, and, as indicated, even Bach himself left some theoretical writings, though fairly rudimentary ones.
As to the 2nd question, it's important to distinguish chord from function. While the 6/3-chord on the 2nd scale degree can be described as vii°6, its function is that of a dominant. That said, in Example 1 there is no dissonance in the strict sense, so it just isn't very helpful to think of it as a 7th-chord in 2nd inversion without root.
That's my take on it, anyway. What do you think? Comment below and sign up to the newsletter if you'd like to receive updates on new blog posts!