As others have said, it was never banned. To clarify diabolus in musica, this referred to the ambiguity of how to resolve it. Harmony had developed enough by the 1700s that B+F could resolve to either C+E or Bb+Gb. But back then, C major and Gb major were still considered distant keys.
Something similar happened in twelve-tone music: certain hexachords ...
Do different modes have the same cadence structure?
In major and minor keys, the perfect cadence is V to I
Correct. For minor keys some write the Roman numerals V i with lower case for the minor tonic. Keep in mind that the dominant triad must be major for a major/minor key perfect cadence.
Will this structure remain the same in a different mode?
Keys use tonal approaches by using functional harmony. The two main types of final cadences in tonal music are known as authentic and plagal.
Authentic cadence in major key: V-I (Ex. G-C)
Authentic cadence in minor key: V-i (Ex. E-Am) (or sometimes v-i (Ex. Em-Am) but very rare.)
Plagal cadence in major key: IV-I (Ex. F-C)
Plagal cadence in minor key: iv-i ...
have a first look at the ending of the piece. Most (not all) pieces end on their basic key.
Start out learning the traditional notation system with Major/minor keys and its sharps and flats. Use the "circle of fifth" for example. Its easier to figure out a special mode then, when it is not fitting into the classical system.
Modes are ...
There is not just one modal style. Do you mean Medieval modal, modal folk, modal jazz, modal rock? I'll address two.
In terms of standards, the clausula vera is the standard cadence in Medieval modal music. I think it is worth noting that even in this early style the mode could be chromatically altered to form a cadence. Your outline of cadences in the ...
In Ionian, the primary triads are [I], [IV], and [V] - just like you've mentioned.
In Dorian, the ^6 degree brings out the Dorian flavor so the [IV] clearly stands out, and I've gone through [i]-[IV]-[VII]-[i] chord progressions in the mode quite often - so in Dorian, I would say the primary triads are [i], [IV], and [VII].
In Phrygian, notice the minor [...
The seven modes we all know are Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian. Modal cadences are quite different from tonal cadences. Modal cadences don't tend to set up a resolution to the tonic chord like how tonal cadences (V-I, IV-I) would do, but rather to show the character of the mode.
The characteristic tones are ^4 in Ionian,...