1) Most of the signal lives in the "bass-ment". At max gain, the 250, like it's sibling the Distortion+, rolls off at 720hz. My hunch is that this strategy was originally adopted to avoid boosting the hum that was typical of many single-coil-equipped guitars in the 70's (although this hasn't been confirmed by undisputable evidence). Whatever the case, use of a bass rolloff that decreases as gain is increased will get you much less clipping at max gain than you were expecting. If you want more grind for your gain, lower the rolloff by means of a larger cap value than the stock .047uf component. A .22uf cap or even .47uf makes more sense. the extra bass will result in more clipping because those mids get to ride in on a much larger low-frequency wave.
2) The total distortion produced is a function of a) the clipping diodes, to be sure, b) the limits of the chip, given the supply voltage and gain, and c) the impact of the output signal amplitude on whatever the pedal happens to be plugged into. Neither the Distortion+ nor the DOD250 were intended to be all-out fuzzes. They were intended to provide some coloration on their own, but induce even MORE coloration from the amp. Use of germanium diodes will, to be sure, result in more clipping at the pedal level, but will impair clipping from the amp because of the impact on output amplitude from the pedal. There is, of course, a balance to be achieved. If you use a trio or quartet of Si diodes, you'll get more output at max volume, but it won't be clipped as much, and there won't be nearly as much compression of the signal as you'd get from Ge or even a simple pair of Si diodes. I find optimum to be a humble pair of Si.
3) The Dist+ and DOD250 are set to a max gain of 213. If you're after sizzle, make the 1M feedback resistor 1.5M and the 4k7 resistor in series with the gain control 3k3. That'll get you a maximum gain of 455, which starts to put you in the serious sizzle zone. Dropping the 4k7 to 3k3 will demand that you increase the value of the .047uf cap, even if you currently like the bass rolloff.
4) Gain is certaily related to amount of distortion, but fundamentally it your signal's "proximity to clip" that matters. If the signal you hit the 250 with is VERY robust (e.g., boosted by a compressor, booster, EQ, or any combination) then you can expect the clipping stage to react more aggressively because what you have fed it does not need very much additional gain to be at the clippin threshold of the diodes. If you feed the pedal unadulterated lipstick pickups, then your guitar is gonna need a LOT of help from the gain stage to reach the clipping threshold of the diodes with any degree of consistency.