Lámpa means lamp in Spanish too!
the audio definitely sounded to me like /O lampo/ :/
That is how the Hungarian a sound is pronounced.
Yes, and keep in mind that it's much more open than an /o/. It's often demonstrated with "hot" in English, I personally find it close to the schwa sound but even more open and a back vowel
Why not egy lampa?
Guess what - because that's not "the lamp", it's "a lamp".