Portrait lens.

The classical head and shoulders portrait lens in 35 mm full frame (FF) equivalence is 85-135 mm, with many centering on the 90 -105 range.  This is based on distance to subject, and lack of perspective distortion that occurs with this focal length range when compared with with shorter focal length lenses.  With shorter focal length lenses, when the distance to the subject is too close, say in a head and shoulders portrait, perspective distortion becomes apparent, the classic big nose small face, and smaller shoulders distortion.

All of the above was described in FF equivalence, which many people can relate to from the old film days.  Now in micro four thirds (MFT) terms, this is why we have kit zooms that end in the 42 to 45 mm range (84 mm to 90 mm FF equivalence) and why Olympus has the 45 mm f1.8 prime lens and Panasonic has its dual duty 45mm  f2.8 macro prime lens (90mm FF equivalent). Panasonic has announced a 42.5 mm f 1.4 (85mm FF equivalent) as has Cosina Voightlander its own 42 mm f0.95 lens.  Olympus has also introduced its wonderful 75mm f1.8, a little on the long end, but still works for portraits...you just have a longer working distance, which could be problematic in a some situations, and really, you might also be able to use their 60 mm f2.8 macro, which as a focal length, falls into the portrait lens range.  With MFT, a 25 mm lens such as the Panasonic 25 mm f1.4 is a "normal" lens (50 mm FF equivalent).  Assuming you do not get too close to the subject to introduce perspective distortion, the 25 mm focal length is usable for portraits, though probably not classic head and shoulder portraits.  As your focal length gets longer, and go towards 40 mm and longer, with MFT sensors, the perspective distortion pretty much goes away because your working distance from the subject becomes greater.

To answer your first question about DSLRs, 35 mm in a FF DSLR is a short focal lenght, a wide angle...not a classic head and shoulders portrait lens, but could work for environmental portraits where the subject is not filling the frame.  Now, on a crop sensor (APS-C) DSLR, the 35 mm would be approximately equivalent to a 50 mm FF equivalent standard lens...a little short for a classic head and shoulders portrait, but assuming you don't get too close to the subject, a 50 mm FF equivalent can take good portraits.  Similarly, a 50 mm lens on a FF is your classic normal lens, but when used on a crop sensor APS-C DSLR, this lens is about equivalent to an 85 mm FF equivalent lens..back into the classical head and shoulders portrait lens focal length.

With respect to your Fujion C mount lens, 35 mm is the focal length, so on a MFT camera, that is equivalent to 70 mm equivalent FF lens, and is quite serviceable as a portrait lens.  The question with C mount lenses is the image circle...you could get vignetting with that lens because the MFT sensor is exceeding the image circle.  Also I don't know about the absolute image quality of this lens.