Tuki (תוכי) is a Tamil word (Tokai) that was imported into the Hebrew lexicon a long time ago, so only for the sake of of being consistent with birds which have a modern convention (that a Tzipor/Tsipor (Ṣipor more correctly) (ציפור) is feminine) of having a noun that has an irregular pluralisation (think for example Shaneem Rabot VeNe`eemot שנים רבות ונעימות), that tuki/tukeem takes this on
No, you can't use only דבר because that would not make sense. You need to conjugate the verb to match the gender and the number of the noun - in this instance it is feminine plural, because ציפורים is a feminine plural word. Therefore, it is הציפורים מדברות. If it were one bird speaking you would say הציפור מדברת.