Is saying "None has the right to be worshipped except Allah alone, without partner. To Him belongs all sovereignty and praise, and He is over all things competent," one hundred times in the morning and evening sufficient for protection from Satan and for recording good deeds, and to what extent is it necessary to combine it with other remembrances to achieve that?

It is best for one to perform all the adhkar (remembrances) if they are able. If one is unable, then they should perform what they can, even if it is only one dhikr, as Imam Al-Nawawi mentioned. The virtue of protection from Satan is achieved by the dhikr mentioned in the question, even if it is recited only once, due to the hadith of Abu Ayyash from the Prophet, peace and blessings be upon him: "Whoever says when he awakens in the morning: 'None has the right to be worshipped except Allah, alone, without partner. To Him belongs all sovereignty and all praise, and He is over all things competent,' it will be for him as if he freed a slave from the progeny of Isma'il, and ten good deeds will be written for him, and ten sins will be erased from him, and he will be raised ten degrees, and he will be in protection from Satan until the evening. And if he says it in the evening, it will be likewise until the morning."