Put the probe ground clip(s) on the negative rail - the emitter of the transistor, for example. Unless I missed something where circuit ground is way above earth ground. Since you are using a lab supply with current limiting, I would back it down to a more reasonable number - what current does the meter measure? 50 mA? Then set to 100 mA.
If you want to be absolutely certain of the circuit ground voltage relative to earth ground, use a shorting clip at the power supply to short between the black and green jacks. I'm assuming you have a legitimate earth ground at the input to the power supply. Since the scope clips are grounded through the scope power cord, you might as well short the negative rail to earth ground at the power supply. Or not... You should get the same results either way.
Page 6-60 discusses rise time measurements:
https://www.batronix.com/pdf/Rigol/UserGuide/DS1000Z_UserGuide_EN.pdfPush the up-arrow at the bottom left of the screen to get to the 'other' Horizontal menu.
Then press the 3rd button down for "Rise Time" or the 4th button down for "Fall Time".
You select the active channel as always, just tap the channel button once until the channel label at the bottom of the screen is highlighted. Or just display a single channel.
The User Manual also shows the use of cursors for measurements. The thing is, you can't find the 10% and 90% points visually nearly as well as the scope can find them mathematically.