The first item is not good for library maintenance because it can potentially give a wrong impression that a page is a wiki orphan.
The behavior you mention is known and as such intended. Links/backlinks only work for links directly embedded in the page's source. That's the way the functionality is working currently.
It would need a major change, so that all relevant data gets updated, when e.g. a template included by another template included by the page changes and adds a link. Same goes for special:search.
That's the internal (programmer's) view. Looking from the outside in (user's view,) the current logic is not very intuitive. One would assume that every link one sees is counted as "real" link. This affects not only backlinks, but also e.g. AdvancedFindPage, PagesByDistance and paths.
In short: I understand the argument, I even feel inclined to view it as the correct way to handle links, but internally this is a large change with far reaching consequences (*). As such, it does not currently have top priority.
(*) Examples: nested templates or a single change in a popular template can possibly affect the link structure of hundreds of pages.
Understood, thanks! I guess we'll leave it as it is right now.