There's no such thing as senseless violence, according to the one who commits it. Characters who kill or torture without at least an internal justification are crazy, not evil. You don't have a reason to kill people in the party or at random, so you don't. This doesn't make you nonevil.
Also remember that just because you're Evil doesn't mean you're a villain. Many Evil characters have no ambitions higher than their own survival and/or comfort; they don't aspire to great power, nor to purge the world of the target of their hate. They're just trying to get by, not so different from the rest of us.
The traditional list of Seven Deadly Sins was originally compiled not so much as a list of inherent sins, but a list of reasons that people sin. This makes it a great source of motives for Evil characters. I prefer to expand the list to nine, adding Fear as Wrath's twin in the fight-or-flight reflex, and Despair because it was actually in the original list; Sloth replaced it later.
Avarice: The key to happiness is having things. I will have it all.
Envy: I deserve it, not them. I will have it from them.
Gluttony: Pity those not at the top of the food chain. I will never be in that position.
Lust: I want to do it all, and I will let nothing get in my way.
Pride: I must be better then them: so much so that my superiority is never even questioned.
Sloth: I just don't want to do it. Let them do it for me. If they refuse, make them do it for me.
Wrath: They will never hurt me again. I will punish them for what they did, and leave them unable to do it to anyone else.
Fear: They must not be allowed to hurt me. (Note the lack of an again here: this is one of the big differentiators between Fear and Wrath, but it can make a huge difference in the character).
Despair: I just want the pain to end. Giving it to others helps.
Also keep in mind that these are core motivations. Any one of them will need to be elaborated upon. What is it? Who are they? How does the character plan to achieve this goal? Also worth noting is the lengths that your character goes to to hide her motives. Evil characters often prey upon one another's weaknesses, and while Wrath-type characters might not worry about seeming weak due to their motives, Sloth-type and Fear-type characters likely would. These folks are likely to construct a facade, often but not always based on Wrath, as a matter of posturing.
Your character sounds like a Wrath-type, with a focus on the undead. Because her main focus is on something that is not so amenable to the survival of humanity in general, she can get along decently well in society, and even be a very useful sort of person to have around. Some might even mistake her for heroic. But she has a twisted fight-or-flight reflex: any slight or injury, real or imagined, runs the risk of touching on that trauma, for reasons that make sense only to your character (if they even make sense to her). She might lash out disproportionately at small threats, or even against things she mistakenly believes to be threats, but are not.
Firstly, you should talk to all your players about the issue outside of a session. You can get some personal impressions first with one-on-one conversations, but ultimately the entire group should sit down to discuss the problems. Make sure the discussion is democratic in nature, though. JohnP points this out in a related question: "The group setting can be dangerous, as it can turn into people digging up old grievances or ganging up on a particular person."
During the discussion you should ensure that everyone is on the same page about how they want the game to be played. The same page tool is a useful set of questions that will drive the discussion in the right direction. Just make sure everyone is fully involved in the discussion and are voicing their opinions clearly (no passive-aggressive bs). If your players are open to compromises a consensus should be reached.
Secondly, make sure your friend is not suffering from My Guy syndrome. If the description matches (and it sounds like it does), show her the link privately and let her think about it. It should help her be more aware of her role as a player and hopefully remedy some of the issues.
You also mentioned your player gets upset as a result of your decisions. This related question contains a lot of suggestions for how to handle players that take things personally, ranging from studying your own approach to kicking out the problematic player.
In the end, though, you are the GM. You are the writer of half of the story, the referee on all mechanics, and the leader in the quest for fun. The way you drive your campaign is part of your style and your players should respect it. They need to be aware that your goal is always to increase the enjoyment they collectively get out of your game. A certain level of trust and respect is absolutely necessary. If this is impossible to obtain in your group, then the group as it is cannot function. Kicking out players or stepping down as GM would be the next steps to try.
Because the GM is so special, though, new players often fail to grasp just how complex the GM role can be, and can at times see him as an enemy and spoilsport. A neat "trick" you can use to show your players what being a GM is really about (that also gives you some rest from the responsibility of being a GM) is to have another person in the group be the GM for a few sessions. It doesn't have to (and most often shouldn't) be the same campaign you're running. Instead, it can be a few sessions of an off-shoot campaign. It's fun for the players because they get the chance to try out new (and often times silly) character builds, and the new GM will discover what it feels to have all this responsibility. Once everyone has GM-ed a couple of sessions, you will all have an idea of who's best at it and will work towards keeping that person as GM in the future. There's a chance it might not be you, but in the end it should result in a better experience overall.
Keep in mind that not everyone is fit for GM-ing, or willing to try at all. Don't force players to GM, and if they decide to try, encourage them to design very short adventures (no more than three sessions). They can always expand on them later if they like it, or end them early if they don't. The player that questions your decisions often probably thinks they can do a better job, so they're likely to accept your offer to prove themselves.
Best Answer
Bluff Works - In Character (IC) Only
So long as Elan and Human are indistinguishable at a glance, Bluff will do what you need. If they're obviously different just by looking, you'll also need Disguise or magic.
The harder part is keeping it a secret Out of Character (OOC). If you don't want the other players to know, then you'll have to take some extra measures.
Poison
You can get away without revealing that you have poison immunity for a long time, because most poisons allow a save anyway. So even a normal Human can shrug off really strong poisons, and you can just pass it off IC by saying you have a strong fortitude or are just lucky.
OOC, you're going to have to roll the fortitude save along with everyone else. The DM will have to know that you're never affected and handle it accordingly, no matter what you roll. The really hard part here is that the players will notice pretty quickly that you're making saves even with a 2 for poison, while not making saves for other things with bad rolls.
You can handle that either by having the DM roll all your saves for you (if you're the only one doing it, then it's obvious something is up), or when you roll badly, pretend you're affected by the poison when you're really not. This will require IC Bluff checks as necessary (to act like you're poisoned), as well as OOC acting like your character is affected.
Not Sleeping
IC, you can pretend to sleep. OOC, you can say you're sleeping when everyone else is, and not many people are going to be awake to question it. If you have watches during the night, take one.
A Ring of Sustenance makes this easier as you only have to sleep a couple hours anyway, but isn't necessary.
Save Bonuses
These only matter OOC if someone wants to examine your character sheet, because until they do that you can just say you have good saves. There are so many ways to get save bonuses that it's not that unusual.
IC, it should never come up.
Power Points to Prevent Damage
IC, you are lucky and some of them just nicked you.
OOC, this is getting trickier. You'll need an agreement with the DM on how to use these without revealing that you're using them to the other players. Maybe you can just do it without telling the DM you're doing it, and do the tracking yourself. That's how I would handle it in the game I'm DMing right now.
The Big One - Being an Abberation
This is actually the biggest problem. You're not a humanoid. Lots of spells that affect the humanoid type won't work on you at all. If someone casts a spell that never fails like Enlarge Person on you and it suddenly fails, questions will be asked.
You'll want to try to suggest those kinds of spells always be cast on other people "for the good of the party".
Have An Endgame
You're probably not going to be able to keep this up forever. IC, you'll fail bluff checks at some point, and the party will catch on. Maybe they'll actually check you for poison, or try to hit you with a buff that fails due to type, or so on. When it happens, you'll want to have a plan for how to explain to them why you kept it a secret.
OOC, the players may notice at some point that something is up. The less you have to have conversations with the DM in private (or exchanging notes and such), the longer you can go without drawing suspicion. So try to work things out between sessions and act as normally as you can during sessions.
But when it does happen, just point out that you wanted it to be a surprise they resolved In Character first.
I've had people do this type of thing in my game (as Changelings and such) and it always worked pretty well. Elan is a bit harder to fit in than a Changeling, but it should make for a fun time.