This answer depends a lot upon the method you use to animate him. Your options are basically these:
animate dead – Core and lowest-level, but applies the very-weak Skeleton or Zombie templates.
Ritual of Crucimigration – From Libris Mortis, this applies the quite good Necropolitan template. On the other hand, it’s a voluntary ritual that gives the one performing it no control over the participant.
animate dread warrior – From Unapproachable East, and thus on some level Faerûn-specific, this spell applies the excellent Dread Warrior template, while still granting the caster control.
Using animate dead is probably undesirable, since it will make him mindless, have 10 Wisdom, and 1 Charisma, and remove most (all?) of his class features thanks to the way Skeleton and Zombie work.
The Animal Companion, on the other hand, cannot be animated with the Ritual of Crucimigration or animate dread warrior, which makes animate dead the only option out of these three. I’m still looking for a better one, though, since the Skeleton and Zombie templates are still weak for an Animal Companion. Ultimately, though, I think it’s best to just leave the Animal Companion alive. Maybe give it the Tomb-Tainted Soul feat, so it heals from Negative Energy (and is harmed by Positive Energy), like Undead creatures, to represent its bond to an Undead creature.
Anyway, your questions:
Animating his Animal Companion makes it no longer an Animal Companion; it is under the control of whoever did the animating. He would be eligible to take a new Animal Companion; there may be a feat or something that would allow the Animal Companion to be Undead, in which case he could re-bond his newly-animated Animal Companion if the animator releases it. He could just keep his (living) Animal Companion, though.
The alignment change certainly isn’t going to be a problem; NE is a legitimate Druid alignment. The problem, at least for animate dead, is that the Skeleton and Zombie templates both remove all existing special qualities and special attacks – there goes your Druid class features.
By RAW, it is lost. Reasonable DMs will allow replacement, probably with the caveat that the new feat was something you could have taken at that time.
No, animate dead does not have any rule that causes level loss as with raise dead. Note that the compulsory templates do have Level Adjustments that will cause him to take longer to level up. As an NPC, though, that doesn’t really matter. Just pay attention to the CR rules.
Ritual of Crucimigration
The Necropolitan template is basically “gain the Undead type, and otherwise get left alone,” which is great. It also has no Level Adjustment, which is even better.
The Necropolitan template cannot be added to any creatures that are not Humanoid or Monstrous Humanoid, so it doesn’ come into play for the Animal Companion.
The Necropolitan template does not change the base creature’s alignment, and does not interfere with Druid class features in any way. See the section on Corrupted Wild Shape, below, for details on Wild Shape.
Feats that cannot be taken by the Undead or those with Con — are lost. Again, replacement is typically appropriate.
The Ritual of Crucimigration results in a level loss, as if a negative level became permanent, and a further loss of 1,000 XP.
Animate Dread Warrior
A Sorcerer/Wizard 6 spell in Unapproachable East, animate dread warrior applies the Dread Warrior template. This template turns any Humanoid into an Undead, with all of his original special attacks and qualities intact. He does lose a great deal of Intelligence and Charisma, but gains some Strength to partially make up for that.
The Dread Warrior template cannot be applied to the Animal Companion.
Dread Warriors are “always NE,” which is a valid Druid alignment, and the template does not interfere with any of the Druid class features. See the section on Corrupted Wild Shape, below, for details on Wild Shape.
“Feats: Same as the base creature, except that the dread warrior loses any feats for which it no longer qualifies.” Again, if you allow the players to replace feats lost like this, then it’s fine for the NPC to.
As far as I can tell, the Dread Warrior template has neither a CR adjustment nor an LA. A Dread Warrior Human Warrior 4 is listed as CR 2, for whatever that’s worth. Anyway, I’d say that this template certainly does make your Druid a fair bit more powerful, so keep that in mind. There is no explicit level loss.
Corrupted Wild Shape: Huh?
Libris Mortis has a feat called Corrupted Wild Shape, which basically claims that you need it to Wild Shape if you’re Undead, because Wild Shape is based on polymorph which only targets living creatures.
There’s a problem with this: it completely ignores the errata for the Player’s Handbook.
Player’s Handbook, page 37
Replace sentence 3 of this class feature with the following text:
This ability functions like the alternate form special ability (see Monster Manual), except as noted here.
Note that some versions of the PHB, including the one I own, have added this errata to the text:
Wild Shape (Su): At 5th level, a druid gains the ability to turn herself into any Small or Medium animal and back again once per day. Her options for new forms include all creatures with the animal type (see the Monster Manual). This ability functions like the alternate form special ability, See Errata.
The most popular website for the SRD (so far as I can tell), d20srd.org, has also incorporated the errata into itself, though it did drop the note indicating that it was errata.
Anyway, the long and short of it is that Alternate Form, unlike polymorph, says nothing about the target being living. An Undead Druid can use Wild Shape without any feat.