What is the ruling on performing acts of worship with the intention of fearing Allah’s worldly punishment, the torment of the grave, and theHereafter, or solely hoping for His reward and Paradise, or with both intentions combined? Does this contradict sincerity, or does it not detract from it? And must the act be performed solely with the intention of attaining Allah’s pleasure, not with the intention of entering Paradise, fearing Hellfire, or avoiding worldly tribulations?

All that you have mentioned regarding performing deeds with the intention of entering Paradise, fearing Hellfire, and seeking Allah's pleasure—all of this is legitimate and part of sincerity. The same applies to worship out of fear of Allah's punishment in this world, for Allah Almighty has warned His servants of worldly torment if they do not obey Him, just as He has warned them of the torment of the Hereafter. The verses in this regard are many, such as His saying: "And if they turn away, Allah will punish them with a painful punishment in this world and the Hereafter" (Quran 9:73), and His saying: "But if they turn away, then say, 'I have warned you of a thunderbolt like the thunderbolt of 'Aad and Thamud'" (Quran 41:13). And in Surat Al-Kahf, His saying: "To warn of a severe punishment from Him" (Quran 18:2). In 'Al-Tahrir wa 'l-Tanwir', it states: "Al-Ba's" refers to intensity in pain, and what is meant here is the severity of circumstances in this worldly life. This is an intimation of a threat to the polytheists regarding what they will encounter of killing and captivity at the hands of the Muslims.