Can Satan and angels know our thoughts or only Allah knows them?

Can Satan and angels know our thoughts or only Allah knows them?
Concise answer
Knowledge of the unseen is prerogative of God. None other than God has knowledge of the unseen independently of God. However, every existent that has been allowed by God to have knowledge of the unseen can read our mind and can see the unseen. In other words, only God has knowledge of the unseen. Whenever He wants and deems appropriate, He opens the gate of the unseen to prophets and angels and whenever He desires, He closes the gate of the unseen to them and forbids them from knowing the unseen.[i]
Most surely, some guarding angels are aware of some of our thoughts[ii], though according to some narrations, some of our thoughts remain hidden to them and only God knows them. Imam Ali (A.S) in his Dua' Kumayl (Kumayl Supplication) says:
«... وَ جَعَلْتَهُمْ شُهُوداً عَلَیَّ مَعَ جَوَارِحِی وَ کُنْتَ أَنْتَ الرَّقِیبَ عَلَیَّ مِنْ وَرَائِهِمْ وَ الشَّاهِدَ لِمَا خَفِیَ عَنْهُم ...»[iii]
"...Thou hast ordered the two noble scribes to confirm whom Thou hast appointed to record all my actions and to be witnesses over me along with the limbs of my body, whilst Thou observeth over me besides them and wast witness to those acts concealed from them..."
According to the holy verse which says "And (there is) a safeguard against every rebellious Shaitan",[iv] the Satan climbed up, due to their satanic trait, to hear the angels and when they came down to earth, they claimed that they had knowledge of the unseen. That is why, the Lord saved the heavens from the evil of satans and whenever they want to climb up, they are repelled with piercing flames.[v]

[i] Najafi, Khomeini, Muhammad Jawad, Tafsir Asaan, vol.4, p. 386, Tehran, Islamiyah, first edition, 1398 A.H.
[ii] Man does not utter a word unless there is an angel guarding and ready to fulfill its mission (i.e. record) at the same instant. Q, 18.
[iii] Tusi, Muhammad bin al-Hasan, Mesbah al-Mujtahid wa Selah al-Muta'abbed, vol.2, p. 849, Beirut, Fiqh al-Shi'ah Institute, first edition, 1411 A.H.
[iv] Saffaat, 7.
[v] Saffaat, 10. Except such as snatch away something by stealth, and they are pursued by a flaming fire, of piercing brightness.