No — that is how it works. Encore knows the public domain classical repertoire well and is learning everything else from the people who use it. When it does not recognise something, your recording becomes a page anyone can answer. Once a person names it, the app answers that piece instantly from then on, for everyone.
Encore follows the melody rather than matching a recording, so it needs more to go on. Five seconds is enough to match a fingerprint; it is not enough to recognise a tune played by someone else.
Two pieces can share a melodic turn, especially over a short excerpt. Try again over a more distinctive passage.
No. The recording is converted to a melodic fingerprint and deleted. The fingerprint cannot be turned back into sound. There is no account, so nothing is tied to you.