K, what I generally pay attention to is fluid writing and engagement, so that's what I'll focus on here. Sorry if I come across a little blunt.
First off, you've admitted as such, but the grammar and language has noticeable flaws and the work suffers for it. There's a couple of sections where there's a flaw in the language that makes reading hard - I have to stop and figure out what you intended with the sentence, process it, then when I move onto the next, I'm stopped again by the next sentence. For example: 'Even in trousers, Viona was stunningly gracious. The long purple vest, the fine white shirt covered by a black corset and the black trousers were her favorite attire when it came to training and if women were not supposed to wear pants, she had not seen many dare reminding her. '
The first sentence, 'gracious' isn't the right word. Stunningly gorgeous might work, but still feels awkward. I'd just say 'Even in trousers, Viona was stunning.' Then when I move on, the next sentence is a bit run-on (too long and rambling), with too many uses of 'and'. The long sentence is trying to say one too many things (The black trousers are her favorite, you're describing what she's wearing & stating that few people dared remind her that trousers weren't appropriate for women.) and could stand to be broken up into two sentences. It's fairly clear you've spell checked, but it didn't always change the errors to the right word - Some issues (Skeptic instead of Skeptical, complains instead of complaints) leave me wondering if it's a grammar or spelling error. Layout quirks (the use of minus signs at the opening of any spoken dialogue, and the intrusion of links into the reading experience) add similar interruptions to the flow of the text. This makes it hard to read.
Then there's the redundancy. This is the second major thing I noticed about the work, and possibly the biggest turnoff. A great many things get said too often. For example, in the sentence I quoted above, you mention the trousers twice. It's pretty unnecessary. In the first chapter, you get a series of paragraphs where you state: "He felt a bit nervous" (First paragraph) "He had not been that nervous in ages" (second paragraph, second sentence). Then the crimes get described as "hideous", "truly gruesome", "he had trouble keeping his stomach in check", "quite an experience". This is a recurring problem, because your updates are short (~800 words?) and infrequent (1 a week), and that means each word is valuable real estate. Another example: Chapter 3, you bring up yet again the fact that Viona is wearing tights. You elaborate on the point, stating that only actors really wear them, and most certainly not educated women, but it's a not insignficant amount of words devoted to something you've said before - 109 words out of an 825 word update covering something you already explained in the previous chapter.
Third; you tend to tell, not show. One of the axioms of writing (one I'm guilty of betraying from time to time) is that your story should demonstrate rather than describe. A lot of text is devoted to just saying how things are. This is common in the earliest chapters (one to four) but it occurs later. For example, you say, often enough, that mathemagicians and technoscientists have a rivalry, but you really elaborate on why, and even before the reader gets a sense of how strong that rivalry is (beyond worrying that Shaw might lose his job), we're already seeing our only example of that facet of the setting disintegrating. Viona's feelings toward him are softening as she sees him with the kids & showing his capability on the way to the pub. This would mean a lot more, for example, if we'd seen prejudice at work beforehand. Shaw, perhaps, enduring abuse at the hands of Technoscientists.
Fourth point: The text doesn't grab me. It reads more like a novel in progress than a web serial. This is a trait/need that sets a web serial apart from regular novel/novella. You need some hook to pull a reader back in for the next installment. This could be cliffhangers, or leaving the reader with questions that are intriguing enough to have them come back for answers.
That last point ties into the ones I made before. It's a little awkward to wade through due to spelling/grammar/layout issues, and what is there is somewhat slow paced with some things seeming to get stressed through repetition rather than demonstration. Just speaking for myself, I found it sort of tough to read through the nine chapters you have there.
On the plus side, you have a very attractive layout, and there's definite room for something, there (though relatively little has happened in 2.2 months of chapters). I'm not saying it's bad, specifically, just that it's a bit slow to start off, and that I think you could do well with a capable native English proofreader to clean up the text.