Feature Vector from an audio signal
Have a good read of various features that can be extracted from popular audio analysis libraries like librosa: https://librosa.github.io/librosa/feature.html


Fundamental frequency (F0) can definitely be extracted. This itself a whole subfield, so google and previous SO questions are your best starting point after reading through what a pitch tracker looks like.
For max phonation time, MFCCs are typically the features computed in the front-end of a speech recognition system, which can give you "phone" sequences and their timing. But this would be a lot of processing as the concept of a "phone" in a speaker-independent sense is quite far from raw audio features one might compute directly on the audio signal (like RMS, ZCR, spectral features, etc)
For timbre, have a read through Bello's notes: http://www.nyu.edu/classes/bello/MIR_files/timbre.pdf


Good luck!