There can never be enough Rarity-centric stories, at least in my humble opinion.

I think you've made two formatting mistakes (font sizing) while typing up Fluttershy's dialogue. It could just be a problem with my phone, though.

Other than that and a few grammar mistakes, this first chapter seems promising.

I'll be keeping an eye on this.

7623497 There was a lot more wrong with it once I looked at it on my phone. I found it much easier to read it there then make the changes as I go along. Should be all done now and Chapter 1 should be good. Going to try and polish up Chapter 2 and have it up tonight!

That is some very not-good characterization.

Hmm, AJ's coming off a little too hard in this chapter but I could believe it as her traditionalist nature racked up a notch or two, to make her reaction after the incident possible or that it's still early along the canon's timeline of Starlight being reformed and thus still not trusted among the rest.

"None of you have to use it if you don't want to. Just know it's there if you ever need it, and if you do. Starlight has my every confidence that it's safe." Twilight tried to put her friends' minds at ease, but Applejack only scoffed and looked away again.

One part of me can understand it, and I think it maybe isn't even about it being safe.

I'm really not a fan of that Cutiemap, mostly because Twilight always thought she wasn't allowed to go with them, and every reason that is probably only there, because it is meant for kids.
Another reason would be, that it made them look like one of those rescue heroes.

"Spike. Write a letter to the Princesses telling them everything that happened, and send them a transcript of today's meeting."

Do you know the feeling, that sometimes you would just be happy if they wouldn't gather an army to rescue someone, search for someone or something like this?
I hope they only find her after they had their little adventure, because I fear it could end to soon if they are searching for them.
I admit I sometimes prefer the quite adventures, and that wildlife, slice of life adventure which seems to happen is looking good already.

I try to explain it a bit better now :
I think I would enjoy Rarity and him having some peace from to many of the known ponys, sometimes I don't like it if they start adding 3 - 10 characters from another world and try to always display all of them which makes it look a bit chaotic.

Sooo that was a good chapter, and the characters felt pretty much alive. Don't take me to seriously, I just start trying to eliminate all that could go wrong if a story starts looking good to me.

Now the only thing you have to know is, that I feel pretty good and interessting while reading this.

"Twilight looked worst than the time she tried to prevent a disaster of some sort!" - yeah - no.
Was this a placeholder you meant to fill in?
There are many times readers would understand with limited explanation. 'the time she tried to understand Pinkie' - even.
Enjoying this, but there are some jarring gaps.

The odds of another friendship mission coming in at exactly the same time is practically nil. Why not just cast it again with “wherever Rarity is” as the location and “when I’ve helped her complete her task or if I say ‘pi is exactly 3!’” as the conditions for return?

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Wouldn't it be possible, that since the map has her cutie mark in all different places it counts her in all of those places. That would mean it could split up anything being teleported to, "where rarity is" into all the different places, effectively tearing a pony to literal shreds.

The stubborn mudhorse strikes again. Too lost in her own hesitation that she couldn't comprehend the instructions given to Rarity about CONCENTRATION. And then has the guts to blame Starlight. You've written Applejack well, btw. I just don't like the mudhorse because of reasons like this. Hard headed and quick to judge.

The dome shrank around her and in a flash she was gone!

The only place exclamation marks go is in character dialogue or character thoughts. Never place them anywhere else. It makes you seem like a poor writer and obviously you are not.

The author really likes their exclamation marks...

Old news I'm sure, but exclamation points are an ornamentation meant for characters when they need to, well, exclaim. Using them in narration is jarring to me and others because it turns what was previously a seemless narration creating an interesting world into a stuttering mess of !. It no longer feels like a narration, it feels like the author is slapping us in the face with each sentence to try and make it more shocking. Most of these paragraphs are great, but so are a lot of things before you cut them into pieces.
Do yourself and your readers a favor and trust in the period. It allows for a world of emotions without patronizing the reader with forced "you should react to this in this way" your writing is good enough without relying on exclamation points, they're holding you back.

O-Okay! Just place your hooves on the table, then state the name of the location you'd like to go, and don't forget to speak very, very clearly, and be sure to have a clear goal in mind.

Alternate story:

Rarity decides her mission is to get an autograph of Ryan Rainclothes. She speaks out, "Appleloosa! I mean Applewood! APPLEWOOD!!" But it was too late. With a flash, the Front half of Rarity ended up in film capital of Equestria, and her hind-end ended up in some bodunk little desert town. All of Equestria mourns, some villain conquers the world without the Elements of Harmony to defeat it, and the nameless woods human succeeds in returning "home."

The End.

Hopefully she isn't too much herself. If she was insufferably ladylike I don't thunk I could have any sympathy for her.

Seriously unimpressed with Rarity at the start. If it was so important that Sweetie Belle use her own sewing kit, maybe you should have helped her find it rather than gpoing off on her. Some Element of Generosity.

Other than that, interesting start.

I'm definitely hooked

"O-Okay! Just place your hooves on the table, then state the name of the location you'd like to go, and don't forget to speak very, very clearly, and be sure to have a clear goal in mind."

Diagonally

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Yeah, due to Applejack interrupting, it is more like "Diagon-", than even "Diagonally".

GET BETTER?....ths chapter already has me hooced...f thngs get too much better theres a lota sleep not gona be happemng

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Alright all right just finished ch2 and now prediction time: This wasn't an accident, Rarity just happen to get a mission and cause the spell to go haywire at the exact moment the human was contemplating suicide...I THINK NOT!!!
The nearly omniscient Tree of Harmony sent Rarity to the woods on purpose to save the human hunter.

harming your children is not a good form of discipline.

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While it made me slightly sick to even read this it's really necessary to mention just how recent in time and local in place that attitude is.

With her often annoying habit of "putting on the airs", Rarity does tend to be one of the harder ponies to convincingly to write about.
I saw the Romancing the Pone being featured, so I poked my nose in to take a look. Seems to be off to a potential good start, but an obvious and immediate solution to getting Rarity back was the very thing that Twilight and Starlight had demonstrated mere moments before: just send Twilight on a self-quest to retrieve Rarity....
But delaying that simple action due to their panic and Twilight's need to research the problem until they actually solve the Heisenberg Uncertainty Problem is something that is SO in-character for the group, I can easily see they won't ever get Rarity back until she's as old as Granny Smith...
but that'll be no problem--they'll be able to keep the same voice actor