Does felii mean "the slices" seeing the double ii makes me think this ('the' plurals) -- if not, what does the work become if 'the' is added?
Yes, "felii" (indefinite article) means slices. If you want "the slices" they would translate to "feliile" (definite article). The singular definite article "felia". Indefinite article "felie". To use "the slices" in the sentence: The slices that I have are small = Feliile mele sunt mici.
Whew! Anyway, it sure looks as though that word is related to the other Romance languages' various words for "leaf", etc. In English, there is "folio", etc.
How come două (which seems female) is combines with felii mici (which both seem male)?
"o felie-două felii" is feminine gender. "Ea e mică" she is small "Ele sunt mici" they are small. Mici" can be used for masculine too "Two small boys — Doi băieți mici"