- Tunisian məlɣiɣa ملغيغة "fontanelle" really is from Berber tamelɣiɣt, a word widely attested in Berber and with no obvious Classical Arabic counterpart...
- but Tunisian gdər قدر "pot" is of course from the Classical Arabic qidr قِدْرٌ, which ought to be familiar even to elementary school students; the Berber cognates cited are borrowings from Arabic.
- Tunisian bəkkuš بكّوش "dumb, mute" is slightly less obvious, but again from Arabic: it's an irregular expressive formation from 'abkam أَبْكَمُ, substituting the dialectally rather productive suffix -uš. The suffix might be from Berber, but the root is not.
- Syrian (and Algerian) dālye دالية "grape-vine" may well be from Aramaic; the word is attested in Syriac with the right meaning (dālī-ṯ-ā "vine-branch, vine"), and belongs to a semantic field where Aramaic borrowings are to be expected from a very early period. Within Arabic, this word was already noted as a regional synonym of karmah in the 10th century by the Palestinian geographer al-Maqdisi.
- However, Syrian mnīħ منيح "good" has nothing to do with Aramaic; it's a local version of widespread dialectal Arabic malīħ مليح, with nasality assimilation. This adjective exists both in Classical Arabic (malīħ) and in Syriac (malīħ-ā) with the meaning of "salty"; in an era where salt was more expensive than now, this naturally tended to imply "tasty". There is no reason to assume either language borrowed this word from the other, since the root is proto-Semitic and the template is productive in both languages. However, only in dialectal Arabic did it go on to develop the sense of "good", which it now has in a wide variety of dialects including North Africa.
- More problematic is Syrian wāwā, a baby-talk word for "pain" used (as far as I can see) neither in Syriac nor in Classical Arabic. Syriac does have wāy "woe!", but so does Coptic - and, if it comes to it, English "waaah!" is closer than either. Onomatopeia is a better explanation than borrowing or inheritance in this case.
The optimistic take on this is that it shows that there's a real public demand in the Arabic-speaking world for information on etymology and on substrate influence. The pessimistic take is that people just want "information" confirming what they want to believe - in this case, that they're not really that Arab after all. (The converse case also exists, of course - recall Othmane Saadi - but I haven't seen as much of it circulating on social media, though that may just reflect my own bubble.) The reality is probably somewhere in the middle.