Would the Berbers in the Sahara convert to Christianity? If so, would this take long than what it took for them to convert to Islam? How does their tribal sctructure fit in an organized religion where hierarchy is important? Might an heretic Christian sect arrise in the North African desert?
Many Berber tribes already did so, since the Antiquity as the romano-berber of the coast that were massivly catholics. Eventually, the other tribes (jewish or polytheists) would be likely absorbed into chritstianization up to the X/XI century.
The Berber society was less tribal than clanic, so you have a "duty" of cohesion that allow mass conversion for the good of the people. If the Christian Berber manage to have a political dominance, the clanic structure would likely help.
Actually you HAD an heresy in North Africa, the Donatism. Even if it was badly crushed since the V century, you could have indeed a Neo-Donatism taking the place that kharidjism had OTL.
And, would trade from Subsaharan Africa to the Magreb develop in this scenario? Would we still see carabans carrying gold and salt across the desert? And what about slave trade?
The trade would be probably dominated by sub-saharian gold, critically for Latinity but also salt and probably slaves (mainly for north african, spanish and byzantine markets).
As this trade existed long before the islamisation of North Africa, most probably that it would continue.
For the slave trade, some could be interested (Visigoths, Byzantines), but I doubt Franks, Lombards, etc would be part of it : 1)It was less expansive to just take slavic slaves 2)Slavery was already being merged with free or semi-free peasantry.
Maybe that this process could take longer than OTL, but in 1000, I would say slavery would be over in western Latinity (and probably in Visigothic Spain too, maybe later).