So in Cyrodiil, alliance matters. Those of you in different alliances will be able to friendly fire each other. If you absolutely insist of doing this with multiple allainces, I recommend using single target skills only or letting one alliance clear the delve for the others.
The skyshards are all in delves or open world, so the number in your group won't matter.
The hardest part will be the six skyshards behind the gates near the scroll temples. In order to get to the enemy skyshards, their gate has to be open, meaning their back keeps are taken. For example, to get the skyshards near EP's Ghartok, DC or AD have to own Arrius and Farragut keep. When those keeps are regained by EP, the gate will shut and you can't get back to the skyshards. This often takes a fair amount of cooperation by your faction. I recommend keeping an eye on your campaign over several days or weeks and be ready to jump on the opportunity to grab those skyshards while the gates are open.