Do note that many furries (myself included) consider themselves human. Humans who happen to like anthropomorphic animal characters. If you answer "yes" to the question "are you a fan of anthropomorphic animal characters?", I'd say you count as a furry.

Now what counts as an anthropomorphic animal is a different discussion.

Furry can apply.

So can Kemono (Beast), the Japanese version of furries.

Though what you describe usually goes under the more specific label of Kemonomimi (Beast ears).

Kemonomimi is what you see in most Japanese media like Tayutama, Kanokon, Nekopara, Spice & Wolf, Hyper Police (though it does have one character that is a full Kemono), and Wagaya no Ō-Inari-sama.

Kemonomimi also has the major exception of being more palatable in anime communities compared to Kemono or Furry. (Just because they are 90% human, 10% beast.)

Here's the real key to this whole dilemma: Do you want to be a furry?

That's really the only question that matters. If you want to call yourself a furry, do so. If you don't, do not. We're not big on gatekeeping, generally speaking. There's no minimum standard of preference you have to meet to be 'allowed' in. Everyone likes different things; the one unifying feature is that we all have some affinity for creatures with some degree of combination of human-like and animal-like features.

Yes.