What is the ruling on prayer if the forehead slips and settles, or settles and slips, but does not continue to slip? And how many prayers must be redone in this case?

Tranquility (طمأنينة) is obligatory in all the physical pillars of prayer. It is the stillness and settling of the limbs for a period of time, estimated to be the duration of saying "Subhan Allah" once. If your forehead settles in prostration for this duration, your prayer is valid.

However, if tranquility is not achieved in prostration, your prayer is invalid and must be repeated. If you cannot ascertain the number of invalid prayers, you must continue to make up for them until you are reasonably certain that you have fulfilled your obligation. This is the view of the majority of scholars.

There is another view held by Sheikh al-Islam Ibn Taymiyyah and those who agreed with him, stating that there is no obligation to make up prayers for someone who omitted a condition or pillar out of ignorance or forgetfulness. According to this view, your prayers would be valid, and you would not need to repeat them. However, the preponderant view is that of the majority of scholars.