Is it recommended to teach children supplications and Remembrances (adhkar)?

Yes, it is recommended to teach them. Sa'd ibn Abi Waqqas (may Allah be pleased with him) used to teach these words to his children just as a teacher teaches children how to write, and he would say that the Messenger of Allah (peace be upon him) used to seek refuge by them after the prayer: 'O Allah, I seek refuge in You from cowardice, I seek refuge in You from being brought back to a miserable old age, I seek refuge in You from the trials of this world, and I seek refuge in You from the punishment of the grave.' (Al-Bukhari).