These questions come up so often in so many different places lol
I'll answer a when I first started reading versus now.
Back when I first started reading, it was the summary that would initially draw me in. (suspense, drama, action/adventure) If it seemed to center around Nick and contained all the guys, if there was no female in the summary or banner - for instance, "Constance Summers was..." *the sound of my scrolling past* Then, most likely i'd give it a try.
Nowadays, honestly I go by author. If I have read your stuff and I have thoroughly enjoyed it, I'll give it a try. Doesn't mean i'll actually stick with it and read it, but i'll at least read the first few chapters to get a sense of whether or not i'll like it. I will occasionally check out a random story if it sounds really interesting or if it's recommended by someone who I know likes the same things I like.
In the older days I rarely stopped reading. I had a lot more patience back then lol If I commited to readiing something I would see it all the way through, even if I ended up not liking it very much.
Now, there are a lot of factors but the main one being if it goes too long without being updated. If it gets to the point that to catch up with the story I'll have to go back and re-read it, I don't bother reading it anymore and then might check it out after it's completed. Just like back in the day, after i'm already invested in a story, i'll probably see it through to the end because if I don't stop reading after about the 10th chapter, that means it has managed to hold my interest. And it's HARD to hold my interest these days. LOL I have no attention span for fanfic anymore.
and in both cases, yes I would tell the author why if they asked.
Both then and now: I always leave reviews for the stories I read. Maybe not on every chapter, especially if they are complete and i'm reading more than one chapter at a time but I think it's really important to let the authors know that someone appreciates all the hard work they are doing. It only takes a minute to leave a review and you could always be the one person who makes that big of a difference to someone who maybe was 'this' close to stopping.
The only reason I will not leave a review is if i'm just trying to figure out if I want to read it or not. If i'm on the fence I don't say anything because I know for me personally, I go by regular readers to know how i'm doing and not how many reviews I have, so I like to really commit to the story before leaving regular reviews.
The other exception for me and this also goes for why i'd stop reading a story, as petty as it sounds, if the author doesn't respond to their reviews then I don't see why I should bother giving them one or bother reading the story. Seriously one of my BIGGEST pet peeves, especially if I see them even once elude to the fact that they want reviews! LOL