All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Dear Brother! We ask Allah to protect you and to help you obey Him. Know that prayers should be performed at prescribed fixed times that are impermissible to violate.
Allah Says (what means): {Indeed, prayer has been decreed upon the believers a decree of specified times.} [Quran 4: 103]
This means that being busy or exhausted does not constitute a genuine reason to delay the prayer, or to perform it after its stated time, or to combine any two obligatory prayers.
For sure, delaying the prayer from its fixed time without an Islamic genuine reason constitutes one of the major sins.
Allah Says (what means): {So woe to those who pray. [But] who are heedless of their prayer.} [Quran 107: 4-5]
Many righteous predecessors of the first three generations after the Prophet (former great scholars of Islam) comment on the above verse saying: “It means those who delay performing the prayer from its stated times.”
But delaying performing the prayer due to oversleeping (beyond one’s will) or forgetfulness is exempt.
Allah's Messenger said: “Whoever sleeps through the time of a certain prayer or forgets it, has to perform it when he remembers it.” [Al-Bukhari]
In brief, it is impermissible to sleep as long as you know that you will not wake up except when the stated time of a certain prayer has gone. In other words, you are not allowed to sleep unless you are sure that you will get up at the fixed time of the prayer to perform it.
As for combining two forms of worship with one intention, here are three different cases:
1) If they (two forms of worship) are united in form and purpose like Ghusl (ritual bath) of Janaabah (major ritual impurity) and al-Jumu'ah, or al-Janaabah and Ghusl of menstruation, or Ghusl of al-Jumu'ah and Eid, there is no problem in such a state.
2) If one of the two forms of worship is not meant in itself like "greeting the Mosque" with some obligatory or Sunnah prayer, also there is no problem in such a state, since the purpose is to make the place busy with prayer. In addition, there is no objection to perform purification for more than one goal with one intention.
3) If each one of these two forms of worship is meant in itself like Thuhr obligatory prayer and its confirmed Sunnah, it is not legal to combine them in one intention; since they are two independent forms of worship.
Imam An-Nawawi said in al-Majmoo`: “There is no disagreement among scholars that one can intend to perform the obligatory prayer with greeting the Mosque or the confirmed Sunnah with greeting the Mosque at the same time.”
As for the two Rak'ahs of Istikhaarah, they are not meant in themselves; i.e. it is permissible to combine, for example, the Fajr obligatory prayer or any confirmed Sunnah with the Istikhaarah prayer in one intention. So, one can perform al-Fajr with such an intention, and then, supplicate Allah with the Istikhaarah supplication.
In this vein, the Prophet said: “Whoever among you intends to do something, is highly advised to perform two optional Rak'ahs, and then, to say … (the Istikhaarah supplication).”
Allah knows best.