Fixed in 1.4.1

Done in 1.4.1

No, it won't be displayed twice. It will be a foldable tree. The tags list will become considerably shorter and you won't have to scroll it several pages down just to get to "programming".
Also note that the tag "c++" will have a fully qualified name "programming/c++", and strictly speaking plain "c++" won't be a tag at all! But CN will be smart enough to automatically expand an entered "c++" to "programming/c++" (or provide auto-complete suggestions if there are ambiguities/name collisions).

I think I must have expressed myself poorly and this is why you misunderstood.
First, saved searches are in a separate ticket here: http://roadmap.cintanotes.com/feedback/15284-search/

Second, there's a notion of subsets in the set theory. A note tagged "c++" is by implication about programming. Tags were introduced because with strict hierarchic taxonomy, an item was limited to just one place in it. But with the model described above, nothing would prevent a note from being part of another tag hierarchy. Continuing the example, the same note can also be tagged "project/myprj1" and "author/johnsmith". I see no drawbacks.

Welcome!

You don't need to press Ctrl+F or grab your mouse. Just start
typing what you'd like to search for.