I'm going to echo a lot of the sentiments that have been expressed already.
It's not a bad start, but there are aspects to your prose that make it harder to read than it should. For one it's all very purple and filled with adverbs. And the second thing is the passive voice. Both of these things bring the pace down and makes everything seem far less urgent. At the start of the story this means I won't be grabbed as fast and am more likely to put the book down.
Another issue is that there is too much tell, instead of show. The information you're trying to dump on me all at once to make me understand these characters and the setting is simply far too much – I don't care about all that at this point. I don't want to sound harsh, but what happens is that in my head instead of the words on the page I just hear 'blah blah blah'. If it's a paragraph I usually get through the section and continue, but I'm getting it for most of the chapter, and that means I start skimming instead of reading and my mind starts to wander away from the story.
Story-wise the biggest thing I want to caution you about is the inclusion of an 'earthling' in a fantasy realm. The 'girl gets transported to a magical realm' plot has a lot of pitfalls. I usually caution against it because a writer really needs to step up their story-telling to make me believe it can transcend the trope.
In the case of your story and the way you tell it there are also a number of assumptions about your setting, right from the first page. The girl is 'an earthling no less', which tells us that the common guard has knowledge of humans and experience with them. At the very least he has cultural knowledge, so travel between earth and this world is not uncommon. She also shows a remarkable knowledge about the place she's at, which also tells us that this world is known on earth.
All of this can be achieved if she is simply from another country in that world and you don't need Earth. The fact that you do makes me assume that dimensional/world/whatever travel is going to be important to the story. If this is not what you are going for you can disappoint the reader.
What I did like is that, apparently, Earth is dying. This is also dangerous, because I'm now more interested in dying-Earth than the fantasy world the characters are in now.
I have to say that I'm only through a part of the first chapter. Because of the above issues I'm having a hard time reading through it. When I get through the whole thing I may have some more suggestions.
To answer a question you had, yes, I think waiting for chapter three to introduce the main POV is too late. The main character drives the story and is the one the reader should care about. That caring should start as soon as possible.
Something you said in your reactions to the critiques so far was very interesting to me. You say:
They defied industrialisation in favour of magic and religion,
How many people can do magic? Because it's fine if wizards forego on technology if their magic can get them everything they need, such as clothes and food. It's also fine for priests to lead a simpler life; the people can care for the god's mortal representatives, or perhaps the priests can also use divine magic.
But for all the other people who are not clergy or wizard, who have to make their own clothes, grow their own food, fashion their own weapons, this reasoning really doesn't apply. People will try to find better ways to do their work, so technology is going to happen. It's one thing to say they haven't advanced as far as we have yet, but to say they consciously stepped away from making their lives easier seems to run contrary to human nature to me.
