I'm not that familiar with gothic law, but I doubt the Caroligians would abandon Salic law so quicky. Heck this could lead to north south split of the Frankish empire instead of OTL's east and west.
Well if I recall the Visigoths converted to Roman Catholicism in the 650s and the Berbers were devout followers as well.
As for languages it would probably become creole fusion of Latin and Berber languages.
1) it could be the one of the frankish kings conquering hispania say the king of aquitine invades and conquers it the most likely division is that of his son in aquitiane and hispania
in the visigothic spain the king chose a succesor and important memebers in the clergy would ratify it the other sons would have property but no spliting or a lot of power as dukes or that the kingdom of the visigoths was more centralized than the frankish ones while civil wars could occur (see the civil war before the conquest of the uyameds)
its not as common any frankish king would IMO adopt the visigothic law inmedietly so that his sons wouldnt have to kill each other once he is dead of course the other sons would not be happy but the eldest would have the support of the power clergy and the other sons would not have a base of power due to no one giving them one after their fathers death if he adopts it .
the visigoths converted in 589 not 650s
2) unlikely if it was romano berbers , tamazing would the looser over the centuries replaced by ibero romance because they would be a puny minority that dint have the cultural clout of islam for people to adopt arabic (you dont need to learn tamazig or other beber languages to read the bible) and the romano berbers would already now latin and thus wouldnt need to change anything sure i can see it having 10% at max influence but dying out as time passes.