1) Can a horde dodge or parry attacks?
No it can´t unless is in their description (hormaguant rules for example).
2) Can a horde attack enemies in melee and make ranged attacks against the same target at the same time? If so would they take the penalty for shooting into melee but also get the bonus for shooting a target within 3 meters?
Yes it can, think that in a big horde not all of the creatures are in melee with the marine at the same time. It is explain in Final sanction.
, and remenber hordes NEVER benefit for the "aim" action
3) Hordes can attack all adjacent enemies in melee and make several shooting attacks as well. Do they use the same structure of full actions/half actions that the players use? For instance can a standard Rebel Horde (magnitude 30) make All Out Attacks against all adjacent enemies while taking 3 Full Auto Bursts as well? I'm not sure exactly what they're capable of.
i don´t think that hordes function like individual characters concerning full o half actions., i have not the corebook yet but i think that one special action per turn (like full atack or lightninh atack) could be the limit of actions for a horde.
If the horde is mangnitude 30, it can do melee atacks to all adjacent objectives (one to each) AND a number of range atacks equal to the first digit of magnitude.
just um givin um an idea of um how it works...