Chapter 1: Nothing too major. Standard plot device for this sort of displacement.
Kudos for the magic being at least partially internally consistent: if it's literally just using water as a portal medium that one can stick their arms through, it makes sense that it can be interrupted by kicking the caster. On the other hand, nothing about the entire premise is explained. It's literally just "lol magic I don't have to tell you shit". Except for a throwaway reference to blood. Maybe the author originally meant to write a romance with vampires instead of a romance with bronze-age princes? :V
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Why the hell do the people in the city speak in a cuneiform script? No, this might seem like a nitpick, but it's a serious fucking problem. So the convention exists: a character is abruptly dumped into a busy foreign location. Everyone around them is speaking in a language that the character and (hopefully, for their sake) the audience can't understand. It works in animation and live-action stuff for obvious reasons. It works in pure-text because you don't literally write out gibberish in a foreign language. In this medium it's a gimmick which actively detracts from the verisimilitude of the setting and clutters the panels.
There are alternatives, easy ones. Use some direct text splashes indicating crowd noise. There, problem solved. Or write in Japanese but use some font-tic equivalent to indicate that it's not actually Japanese they're speaking. Those are not novel ideas.
On the former point, it's highly unlikely that the script is actually associated with the Hittites at all, and laughable to think that it not only is, but is more or less intelligible. There was no reason to use it, either, and other reasons not to. It indicates, I think, a desire to give an impression of a vibrant period setting without actually doing any of the work to create such.
The chapter ends with the main character running up onto a massive wall of doubtful historical accuracy (but possessing a remarkable lack of guards) and screaming to the sky "Where am I!? yadda yadda". The author-narrator helpfully abuses that to segue into a condescending answer directed at the audience. Or maybe it was just the translation and the original text wasn't so snarky. But "if you don't know where Anatolia or Turkey are, go look at a map [dumbass]" seems to speak for itself.
Up next time in Dice Hates Manga: Red River Chapter 2, in which our heroine runs from a bunch of faceless h-doujin zombie pirates guards, meets our first eye-candy (with an alarmingly narrow head), gets chained to a pillar years before the Star Wars prequels made it cool, loses her clothes, and is saved from beheading by Alduin's arrival.