How should a woman make up prayers that she missed two days from delivery?

All perfect praise be to Allah,The Lord of The Worlds                                                                                                                                                                        It is prohibited to delay prayer beyond its prescribed fixed time, therefore, the woman in question is obliged to make up missed prayers after delivery and confinement i.e. once she becomes ritually pure. And Allah Knows Best.

Is it permissible for a young man and a young woman to enter into a covenant as a married couple without having a true seclusion (Khalwah) until their marriage contract is officially concluded?

The relation which isn`t based on a marriage contract is forbidden, and entering into a covenant as a married couple is unaccounted for and is from the evil suggestions of the devil.

Is wearing a cap permissible for boys, or girls?

All Perfect Praise is due to Allah, The Lord of The Worlds.

In principle, anything is permissible sol long as there is no Sharia evidence prohibiting it, thus wearing the cap by boys is permissible as long as it isn`t done in imitation of the disbelievers. Moreover, a Muslim woman should avoid all that which attracts the attention of men because whatever leads to the forbidden is forbidden. And Allah Knows Best.

What is the ruling on the existence of cattles' marketplace of (Sheeps, cows and chickens ) inside a graveyard?

Graves must be respected, and it is not permissible to sit on them or show any disrespect. Establishing a marketplace within a cemetery is undoubtedly a form of disrespect to the deceased and is not permissible. Such actions should not be tolerated. And Allah Knows Best.