How can missed prayers be made up in the form of the number of rak'ahs only, without distinguishing between the prayers (Dhuhr, Asr, Isha), and is it sufficient to make them up with the intention of making up a four-rak'ah or three-rak'ah prayer?

The missed prayer that is to be made up (Dhuhr, Asr, etc.) must be specified, as this is a condition for the validity of the make-up, and making it up without specification is not sufficient. If the worshipper forgets a prayer from a day and does not know which one it is, he must repeat the prayers of a day and a night. This is the view of most scholars, because specification is a condition for the validity of the obligatory prayer, and this cannot be achieved except by repeating all five prayers.