I have both the LCD-XC and the AEON 2 Closed. I can help you with some of your questions.
2) To start off, the LCD-XC has a slightly grander sound, with a larger stage in both width and depth. In terms of resolution and detail retrieval, both headphones are equally capable in this category. The AEON 2 Closed has a marginally more robust low-end, however, with bass that is adequately punchy, with decent slam and impact. Both drivers have a classic planar bass profile, with relatively quick decays and fast transients in the lower registers.
However, the Dan Clark headphone has a more balanced signature - this is especially apparent in the lower midrange, where a lot of the energy is lost in the LCD-XC, especially with male vocals. When I listen to songs featuring both male and female voices, the Audeze presents a stage where the male singer is located, audibly, several metres behind the female vocalist.
The highs on both headphones are clear, with a little sparkle up top. Both headphones lack a brilliant treble presentation, but they aren't found wanting in this section either.
Comfort-wise, the AEON 2 Closed embarrasses the LCD-XC; it is both lighter and more comfortable on the head.
All in all, if you're deciding between these 2 headphones, I'd say that you should save quite a bit, and go with the AEON 2 Closed. In terms of technicalities, it's almost as good as the LCD-XC, but you get a more balanced sound that plays better with myriad genres of music. The Audeze, on the other hand, suffers a lot in vocal-driven tracks, especially male-dominated ones.
3) No, the bass on the AEON 2 Closed is punchy, with fast beats. I actually enjoy the bass presentation on the Dan Clark headphone.
4) I have a Mojo, but it has not been used in a (long) while. Let me see if I can get it charged, and I'll get back to you on that.