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?
Yes and no. It depends on the harmonic style and whether the cadence is kept purely diatonic or is chromatically altered.
As you rotate the diatonic triads through the various modes the triad build on the dominant will change through the three different chord qualities: major, minor, diminished. Only those modes with a major dominant will have the perfect cadence available as a diatonic option: Ionian and Lydian.
However, in Medieval modal style musica ficta is used to add accidentals to the
^7 scale degree in the other modes to create a proper cadence, a clausula vera. A clausula vera is not exactly the same as a perfect cadence, because it doesn't have the descending fifth in the bass, but it is essentially the same major dominant to tonic harmony.
In modal folk music the
bVII chord is often used as a kind of substitute dominant in cadences like
bVII i. Obviously that isn't a perfect cadence, there isn't a
V chord. I think the common use of the
bVII i cadence is harmonizing a phrase ending
^2 ^1, from that melodic perspective it is serving a similar purpose as the
V i perfect cadence, but with a substitute chord.
E Phrygian Mode in the key of C (E F G A B C D) ...the scale would be iii IV V vi viio I ii iii (expressed relative to C major).
You should use the Roman numerals to start on the tonic so the
E minor chord is
i and the full list of chords is
i bII III iv vo VI vii, the dominant triad is diminished and the seventh degree triad is minor.
So would viio to iii be a perfect cadence?
No. Let's re-label that to
vo i. It's not a perfect cadence, because the dominant isn't major.
The clausula vera for Phrygian would be
The folk cadence (for lack of a better term) would be
II i or to make the Phrygian quality clear use a flat sign
Some answered questions posted after this one cover many of these point separately: