You won't get the layout the same, as the screen width in portrait constrains what can be done. You've still got almost all the same information there, it's just laid out differently and maybe presented slightly differently.
Maybe don't make such sweeping assumptions about whether or not others are being honest. Just because you disagree doesn't mean others are being dishonest. What a horrible mindset to have.
Do you have your browser set to delete cookies when you close the browser? If so - that's why. Your logged in state is stored on a cookie on your device. Delete the cookie, be logged out.
Edit: ahhh, see you figures it out. And yes, Incognito mode deletes cookies on close so that'll have been why.
Are you seeing new ones since you made the changes, or old ones from before? The old ones will stay, but you shouldn't get any new ones. Unticking all those boxes was one of the first things I did last night and I'm only receiving the alerts I want (very similar to what you want).
It's actually quite easy once you spot it (although oddly not quite as easy as it was on vB 4). Click / tap on the "+Quote" link on each post you want to quote. Then start your reply, there should be a button appear that says "Insert quotes..." - click that and it'll handle the inserting.
Quick question: do you have your browser set to delete cookies on closing? If so - that'll be why you have to login whenever you return. Your login state is stored on a cookie on your device, if you delete the cookie you'll be logged out.