The bike was measured with the wheels off actually.
I re-mearured everything today. Wheels on this time. But my inclinometer is [+/-] 1 degree, not the most precise device, but it's better than nothing (digital ones were too expensive for the little use they'd get) - so any fractions are guesstimates. Head tube angle appears to be actually a fraction over 76 degrees, seat tube angle a fraction over 77 degrees. Sorry for the mistake.

Co-planar. All 3 string segments were co-planar. You can sight that out quite well. Why don't you give it some thought as to how you'd do that accurately? Hint: the string goes through the front dropouts, and from each dropout, drapes over the stem/extention.

BTW, the handling on this track bike appears less than ideal. It appears not to be conform to conventionally accepted geometry standards. I merely answered a question here, but there is nothing mission critical about this. So according to your expertise we have 2 inches of trail... I think that with a little more trail, the bike would handle much better (on the road). But then again this is a real track bike, not some commercial knockoff destined for bike messengers riding on pavement with their singlespeeds. And on Montreal's velodrome, this thing was agile as hell. Accelerations with the stiff tubing was better than anything else I'd ever tried. We had 49degree banks, and I used to plunge down from their summit, be able to pass someone on the inside at the bottom at full speed, which made for a very sharp turn, on an incline (and leaning the wrong way to make the turn), and this bike always handled beautifully. Not to say that I didn't get a scare sometimes while doing that - but it never let me down in even the toughest of situations.