Thanks for sharing the detailed description to the explain the issue.
I have focused on both the issues you have mentioned above. Tried exactly same as its explained, but none of them is reproducible.
Checked with the latest version of Acrobat DC on Windows-10
I assume you are experiencing these problems with a particular document.
1- As horizontal line shown above, that seems fine. It should be like this when you select the "Shows gap between the pages" and your pages are aligned as "Two page view"
For better experience you may select "Tow page scrolling" and "Show gaps between pages"
It working fine at our end with these page display setting.
2- When you uncheck "Show gaps between pages" that should not effect the number of page flips.
When "Two page view" is selected and you press the Right arrow that should bring the next two pages with a single click whether "Show gap between pages" selected or not.
Its tested at our end and working fine.
If its causing trouble for you, then would suggest you to check with a different file that has multiple pages.
Also see if there is any pending update, Open Acrobat>Help>Check for update.
Hmm... These two issues appear only for "Two page scrolling" view. For simple "Two page view" case everything is OK.
Also I have just discovered that the first issue (vertical offset when pressing "Page Up" or "Page Down" buttons; "Show gaps between pages" and "Two pages scrolling" enabled) appears only when there is some space on the left and right sides of the screen (this is a usual thing when pages are narrow but long). In that case there is a vertical gray (background) line on both sides, See my video below (in this video I pressed "Page Down" button multiple times):
That happens with all my pdf documents. Could you try to reproduce this?