It's said that the maids don't do much around the mansion and that Sakuya does most of the heavy lifting, Sakuya who also pulls double duty as a babysitter from time to time as you see in the upper left picture I'd posted.
From my understanding the fairy maids are allowed to live there with all the amenities, food and such as long as they clean up after themselves and do enough housework to earn their keep. For example the fairy trio tried to infiltrate the mansion with intention to mooch and they got ousted by Sakuya since they didn't actually do anything.
Fairies don't actually have to eat and can just make magic houses in trees, so it's a simple assumption that they work there because they like it there. There's more details on this in the sources on the wiki.
The hobgoblins had nowhere else to go after being chased from the human villages, and that's pretty much where the book ended with that one panel of them winding up at the SDM. While it looks like Remilias giving them a hard time on their first day, consider that Reimu wanted to just no questions asked exterminate them just because of their appearances. That whole chapter was kind of fucked up how the girl versions of the hobgoblins were treasured and they instead got treated like garbage. Made me feel bad, so I'm glad that worked out for them.
As far as Patchouli, Meiling, and Sakuya go, they appear to be on fairly casual friendly terms so it's more likely that she also considers them her friends than as just servants, in particularly Patchouli who is outright stated to be her friend.
As far as why she behaves like that, she seems to like playing the role of the "big bad vampire" without actually doing anything seriously evil, it's the traditional "youkai do what looks like really bad things from the perspective of regular humans." The "meteor targeted to fall on the mansion" was heavily implied to just be her doing chuuni stuff.
There could be many reasons why she does this, especially when you consider it's quite likely vampires are definitely sustainable beyond the barrier without her having to do much of anything, I have some theories for this but they lean towards headcanon so I'll try and abstain from most of that, though I believe it's that she wants to be respected and/or feared.
It also ties into the rest of the Gensokyo incidents in which the "youkai do bad things/say hello via incident and "eat humans" thing because of the theorized "youkai need humans to be scared of them to exist" thing. Whether she does this for fun, because it parallels with her own interests, or because she's secretly helping out her friends even if it's just her more immediate ones in the mansion or even whether that's just an unintended side effect, who can say.
The worst known things we know she's done is the scarlet mist and the moon invasion, and those did not seem enacted with malice in mind so much as simply following her own silly whims without thinking of consequences (then again, saying hello in Touhou is by causing incident traditionally). I imagine if she'd have succeeded in "conquering" the moon with her "army" of 3 maids, Sakuya, and herself, life on the moon would not have changed at all save for having them acknowledge her as their new leader and placing a flag on it or something as that sounds like the sort of thing she'd do.
If the "rampaging vampire incident" precursor for the spellcard duel rules had any truth to it being her, it probably went almost exactly the same as the moon invasion did.
At the beginning of her story in IaMP she does her traditional act of "I'm going to go do the bad vampire things" but in actuality she's trying to thwart Suikas non-stop party incident.
While you may be accurate that she can most certainly be selfish, that is probably the worst of her personality, as she clearly also cares about the health of even the maid fairies. I'm sincerely doubtful that anything she's done has been for outright malicious reasons, as her motives seem to be more about satisfying her silly whims than actually seeking to harm others.
Not many seem to agree with this sentiment however and will frequently paint her as one of the worst sentient beings in Gensokyo in the fandom.