This might be a factor. What’s considered an “ordinary sized novel”? Books are generally getting longer on average. It used to be Stephen King novels were considered “door stops” because of their typical length, but nowadays, King’s books are just average in size.
Back when I was in high school, a novel every few days wan’t unusual, but they weren’t 400-800 pages, 200 pages was more typical.
Oh, I absolutely count books I didn’t finish. On Goodreads, if I attempt a book and don’t like it, I mark it as read, and also include a review saying I didn’t finish it (often including the page number on which I gave up). I use the “read” tag mostly for my own use, and if I tried a book and didn’t like it I want to make sure I keep track of that so that I don’t ever forget I read it and attempt it again. And yes, it inflates my read count, but that’s not really something I take pride in anyways. (I probably ought to get out more, but reading is just so easy and comforting.)
Also, if someone asks me if I read such-and-such book, it’s perfectly natural to say yes and follow up with “I gave up on it halfway through because the plot wasn’t going anywhere.” Just about any time that someone asks if you read a book, they’re asking because they’re interested in what you thought of the book.
Sure, but you could easily reply “No, I gave up on it halfway through.” to the question of “Have you read X?”
Not saying you’re wrong, just that my opinion is different and that I added an exclusive “did-not-finish”-tag to Goodreads’ built in ones of Read, Currently-Reading, and To-Read, which would solve your “keeping track” problem without committing heresy! 
ETA: You can set any Goodreads tag to Exclusive, which makes it a status equal to Read/Currently-reading/To-read for a book.
Gotta go with wind here. Giving up halfway through because the book is boring, or overly bad, or stupid still gets you “Read it” credit in my mind. The only exception would be if the person asking the question was about to test you on it, like your English teacher.
But can you still give it a one-star rating?
I read at least one book a month. And that would include any introduction note from the author before the story begins and/or an author note at the end. As others have said I share the view that if you have not completed a book then it doesn’t count as having read it. I do not complete every book I start. If I do not complete it I will not give it a rating on the Goodreads website. Sometimes a book just doesn’t interest me enough to keep going but it would be unfair on the author to badmouth it just because I decided to give up on it.
I actually read much more now than I did ten or fifteen years ago. Maybe that’s a consequence of becoming older but I actually feel more satisfied now finding a good thriller book to sit and read on a Friday night until I fall asleep than binge-watching a TV series or going to the movies. The amount of time is the same. If I am reading a locked room mystery (which those who are regulars on the Khadaji books threads might know I am a big fan of) I will try and read it from start to finish in one night. I think those kind of themes have to be read in one go and you might just compel yourself into doing it by thinking you’ll just do one more page but before you know it several hours have passed and you have finished it. That happens to me every so often 
Certainly.
I still read two books or so a week, though they’re generally easy reading genre books. Books with denser language take longer, and books in German take a good couple of weeks, half an hour or so a day, but I’m not a native speaker.
Reading the whole book is what counts; for non-fiction, it does vary more, though. Those I generally read the whole of, but a few have sections that I’m more interested in than others. Also they take longer to read because I’m happier to dip in and out of them. In terms of actual hours spent reading, they’re pretty much the same as easy reading novels.
I will DNF a book in Goodreads and will mark it as read, but won’t put a date on it so that it doesn’t count toward my running total for the year.
If a book sucks a lot, but I do skim it to the end just to see how it ends, I will count it as read.
Finally, as for what counts as a complete book for ones I do complete, I don’t count forewords - in fact, I don’t even read them, because some annotators, particularly ones in the field of capital-L Literature, think it’s perfectly reasonable to spoil the contents of the book in order to make some highfalutin literary point. Academic bastards.