Agree. So long as you're not increasing frequencies to unachievable output levels (i.e. increasing levels in the analog stage) then there should be no measurable distortion added.
Not sure I've explained that well... What I mean is that most of the quality players out there are able to adjust levels in the digital signal without inducing any clipping or distortion. If in doubt, you can also use your EQ in a subtractive way only (i.e. reduce frequencies only, don't increase them) which will prevent clipping and distortion in my experience. For example, if you want more bass output, you can use your EQ to reduce the high frequencies while leaving bass frequencies at 0dB. This shouldn't introduce unwanted issues.
Yep, clipping is the only real danger with a decent eq implementation (like the 24 bit dsp one built into a lot of DAC chips.) And the answer is the same as it always - don't push volume up past your amp will handle - so use negative eq, or adjust volume down if you run into problems.