: How to improvise chord progressions? I know how to make a chord progression, but when playing in a certain mode, how can I know instantly which chord is the ii and which chord is V, etc?

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First of all, the ii and V chord are very specific chords not all modes have for example, Phrygian does not have a ii chord (it has a II or bII depending on how you look at it) or a V chord (it has a v instead). If you are however referring to the concept of tonic, predominant, and dominant then the modes do have them in some way shape or form, just not in the same sense major does.

Second if you really want to write and improvise chord progressions for modes you need to understand what gives each mode it's flavor. A very simple example is in Phrygian, the bII chord really brings out the flavor of the mode and is really good for getting back to the tonic chord and can be viewed in some ways as a dominant chord so a simple way we can take advantage of this in C Phrygian is:

Cm - Db - Eb - Db

Nothing very spacial, but it brings out the flavor of Phrygian and keeping the bII-i in mind when wanting a progression to sound Phrygian is key.

In general you don't need to say in one key/mode when making a progression or improvising one. If you understand the ideas of harmony well enough, you can create a near infinite progressions using ideas like modal mixture, secondary chords, tritone substitution, and passing chords.

Listen and analyse progressions you like and you'll find things you like and thing you don't and you can base you chord progression improvisation off that. Also it's good to not that how you voice the chords also affect how your progression sounds and you should be aware of that also.

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I would suggest learning to play the full authentic cadence in a simple key (for instance in C).

This include:
T-S-D-Tp-Sp7-K6/4-D-D7-T:

When you master that by memory on the piano, try to transpose it to G and F key. There is no other shortcut, the mastery of music asks for practicing.