From what I have read before, it is said that the Vandals were conquered by the Byzantine Empire (I would assume they integrated with the Byzantine culture later on) but did any of them actually stay in Algiers? If they did, what happened to the women and were they all living peacefully once Islam came or did they die out/integrate before the rise of Islam?
The contemporary historian Procopius reported that the Vandals were deported in two waves, the first taking place shortly after the war was over in 534, seemingly involving only fighting men to be reorganised into cavalry regiments on the eastern frontier, the next in 540, which included both men and women. There are no sources for Vandal remnants after this, so unfortunately it is impossible to answer your question with evidence directly drawn from the sources.
We can however say a little bit more. When we say that the 'Vandals were deported', we really only mean the military elite that stood at the apex of social hierarchy in North Africa, as that is what all the sources say. We don't hear of Vandal merchants or farmers - yet men and women of Vandal origin practicing these trades must have existed. We should therefore see 'Vandal' more as a social status, rather than an ethnicity. Indeed, as Jonathan Conant has rightfully pointed out, by the early sixth century the Romano-African and Vandal communities were becoming increasingly integrated - or, at the very least, the sources did not see the point of explicitly saying who was a Vandal and what identifiable traits he had:
As a result, we do not really know how long distinctively Vandal cultural traits survived in Africa – indeed, we scarcely know what kind of traits to look for – because, like most of us, the Romano-Africans who produced the extant literary sources viewed the world through cultural lenses that preconditioned what they were able to see.
Like in the other 'barbarian' kingdoms, contemporaries continued to view events in a Roman lens. Yet we also know that the Vandals themselves adopted Roman trappings, for example by sponsoring poets to praise their kings in the most exuberant terms, so there is really no way for us to distinguish a person of Vandal origin from a Roman, which I think explains why we can't find any trace of the Vandals after the 530s. As we don't really hear of the 'ordinary' Vandals, we can only assume that they became integrated into Romano-African society. As a result, when we say that men were deported east in 534 we only mean that a very small section of society was removed, people who were Vandal by status, not Vandal by ethnicity, if you know what I mean. In this case, it meant men who obviously 'Vandals' by virtue of their status as nobles, even though many ethnic Vandals remained. The women stayed too, for Procopius reported that imperial soldiers who married Vandal women mutinied in 536 when the emperor legislated to return land from the Vandal 'heretics' to 'orthodox' Christians. This led to a long-running revolt and was why the general Solomon decided to deport the Vandal women as well in 540 - which is actually an indication that the remaining Vandals in Africa held a great deal of influence, as soldiers were willing to mutiny to protect their new-found wealth. Again, we cannot assume that this deportation involved everyone of Vandal descent, as in this instance we can only say that this process involved landed women, who were presumably deemed Vandals because of their influence and wealth in African society.
With that out of the way, how did Africans, who included people of Vandal descent, react to the rise of Islam in the seventh century? The answer is again difficult to get at, as the evidence for this period is both minimal and fragmentary. What we can say is that Romano-African sources in this period all identified themselves as Romans and as imperial subjects - even if they disagreed with the emperor in Constantinople, they still subscribed to the imperial ideology and sought to persuade the emperor to change their policy. The most drastic case would be the exarch (local governor) Gregory, who revolted in 646, but only against Constantinople's failing military policy and what appeared to be 'heretical' leanings. There is no evidence that North Africans sought to divorce themselves from the larger imperial framework in the seventh century. Based on this, I think it would be safe to postulate that people descended from the Vandals, of whom there must have been many, behaved no differently from their neighbours.