I know it's rated up to 300ohms, but some have mentioned here that they lack the proper voltage to drive many headphones in that 250 range.
I'm still new to all this. What exactly do I have with the Fiio e10?
(Can I pair it somewhat effectively with Beyerdynamic DT880 or DT990 250ohm??)
Yes, it should work reasonably with those headphones, if you do not need very high volume (105+ dB). "Maximum impedance ratings" are rather meaningless, by the way, since there can be large differences between headphones of the same impedance regarding how easy they are to drive, but in this particular case the amplifier should be OK.