Is it permissible to ignore the whispers of disbelief (kufr) and polytheism (shirk) and not seek forgiveness thereafter, and likewise, to ignore the whispers regarding not mentioning Allah’s name over food and praising Him after it, knowing that they are very disliked and recurrent?

These whispers do not harm you nor affect your faith, as long as you dislike them and are repulsed by them. In fact, your dislike of them is proof of the sincerity of your faith, and you will be rewarded for striving against them. You are not required to recite any dhikr after them, and completely ignoring them is the correct approach. Say "Bismillah" once before eating and similar actions, and do not repeat it. There is no contradiction between taking medication and ignoring whispers; organic medicine may help in recovering from this ailment, and taking it is in compliance with the Prophet's command to seek treatment.