Is it correct to use the word "سلبك" (took away from you) in the saying: "If Allah takes away something precious from you, He will give you something more precious," or is it considered ill-mannered towards Allah?

There is no harm in this phrase; it is well-known among the Salaf. Its evidence is the saying of Bishr ibn al-Harith on the day his sister died: "If a servant falls short in obedience to Allah, the Almighty and Exalted, Allah will deprive him of those who brought him comfort." It has also been reported in elevated (marfu') hadiths, including the sacred hadith (definition) (Hadith Qudsi): "If I deprive My servant of his two beloved eyes, and he is content with them, I shall not be pleased with a reward for him less than Paradise if he praises Me for them." And the saying of the Prophet, peace and blessings be upon him: "If I test My servant with his two beloved ones (eyes) and he perseveres, I will compensate him for them with Paradise." And his saying: "No servant is afflicted by a calamity and says: 'Indeed we belong to Allah, and indeed to Him we will return. O Allah, reward me in my calamity and replace it with something better,' except that Allah will reward him in his calamity and replace it with something better for him."