Points of Light
Yes, it does. It’s called “Points of Light,” and my understanding is that it’s basically Greyhawk (Gary Gygax’s original setting for Dungeons & Dragons) with the Gygaxian serial numbers filed off so Wizards can avoid paying them royalties, or something like that.
The core books use this setting. Most supplements use it too, though for the most part they strive to be generic enough to be reasonably added to many different types of settings.
I want to include a quote here by BESW, originally made as a comment to this answer, because I think it’s particularly relevant:
I think it's worth mentioning that the Points of Light setting is deliberately fuzzy on the details. IE, yes, there was a war between dragonborn Arkhosia and tiefling-led Bael Turath a long time ago, but whether that's a thousand or five thousand years ago depends on which article/book you're reading. This is done to take some of the "get it right" pressure off the DM and discourage players from telling the DM that his worldbuilding choices are wrong.
This is one of the better ideas that Wizards has ever had, in my opinion, and you should feel free not to worry too much about matching your campaign up with the “official” details. This was always true, even in the more well-defined settings, but a lot of DMs, especially new ones, felt like they had to match everything perfectly.
Setting Specific Material
The only supplements that don’t use Points of Light, appropriately enough, are the setting-specific books, like books for Eberron or the Forgotten Realms (Faerûn is a part of the Forgotten Realms). There’s not any particular reason why you have to avoid the material from those books in other settings, mind you: they may have been written with a particular setting in mind, but that doesn’t mean you can’t incorporate them into other settings.
For example, the Artificer is kind of the iconic Eberron class, but while Eberron is largely built on the backs of Khorvaire’s Artificers, there’s nothing saying that the Forgotten Realms couldn’t have a fair few Artificers walking around. They’re just not quite so ubiquitous as they are in Eberron, so you haven’t seen the magitech-ish revolution in the Forgotten Realms the way you have in Eberron.
As another example, Dragonmark feats are balanced socially rather than mechanically for their intended setting: getting a 4e Dragonmark means you're socially obligated (or being hunted by people with social obligations re: Dragonmarks) and have effectively handed the DM a "tug my PC around" card. Outside of that social context, Dragonmarks are a little overpowered mechanically (read: nearly on par with Expertise in terms of "why doesn't every PC have one of these?”) without extra work by the DM.
The only setting that really doesn’t play nice with others is Dark Sun. Dark Sun changes a lot of the core assumptions about the world, and a lot of Dark Sun material exists to support those different assumptions. It’s been important to Dark Sun, for a long time now (at least since 2nd edition), that it’s completely cut off from any wider cosmology (in 2e and to a somewhat lesser extent 3.x, all settings were generally sub-settings within Planescape, at least from Planescape’s point of view). Again, though, that does not mean you cannot mix Dark Sun with other settings – it just means you have to be more careful about it.
Pantheons
For the most part, the pantheons are separate, though if I recall correctly, Points of Light and the Forgotten Realms have a fair bit of overlap. Eberron’s gods and the like are certainly completely separate, and Dark Sun... only kind of sort of has gods at all.
Changelings
I don’t know of any particular mention of Changelings in the Forgotten Realms or any place where Changelings are explicitly included in the setting, but they’d hardly be out of place if you wanted to include them.
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.
Best Answer
It really is up to you. There's nothing in the rules that'd prevent it - 4e doesn't enforce alignments. That's a departure from earlier editions, where alignments had mechanical meaning. In 4e, they are there purely for flavor and you don't need to worry about breaking something by changing them.
There's nothing in the nature of goblins that makes them evil, and even if there was you could change that as it's your world. Even in some other editions, when they say "Always Evil", that's meaningless. If that line bothers you, make up goodlins. There are, after all, good undead in D&D 3.5.
Not everything is quite as variable, though. Demons are usually beings of pure evil. Saying demons can be good has ramifications. No one cares about the goblins.
So why are goblins evil? Because that's the stereotype, and a game has to fulfill stereotypes before it can deviate from them, or at least that's the approach D&D tends to follow. In the world you describe, most would perhaps be evil because those are their cultural norms, reinforced by social injustices of others. A goblin's strive for goodness against such forces would make for a compelling story.