Regarding the Barelvis belief, what does it mean that the Prophet (ﷺ) has the authority to do as he desires as granted to him by Allah.

Without a doubt, there can be no better explanation of the Barelvis[1] creed than that of the founder of Barelvism himself, Ahmad Raza Khan.

He stated in his own works:

"The Prophet (ﷺ)  fulfills all types of needs. Indeed, all the affairs of this world and the hereafter are in his hands!"[2]

"Indeed, the keys of the creation - all of them - are in the hands of Allah's Messenger (ﷺ). He is the owner of all, he is the great deputy of the Omnipotent One and he is the one who possesses the word, "Be!""[3]

"The Prophet (ﷺ) is Allah's greatest vicegerent and he is in control of the heaven and the earth!"[4]

For more information in English, see Shaykh Ehsan Elahi Zaheer's work on Barelvism some chapters of which has been translated:

http://www.goodreads.com/book/show/13397670-barailwiyyah

Of course, their excuse that they believe it was Allah who granted him this power, knowledge of the Unseen, etc is totally irrelevant since even the pagans of the Pre-Islamic Days of ignorance did not believe that their idols or the saints they represented wielded any power independently of Allah. In fact, they did not make any such claims in regard to them like what the Barelvis make for prophets and saints which contradict Tawheed-ur-Ruboobiyyah.[5]

We seek refuge in Allah from misguidance.

References: 

[1] http://www.wordaz.com/barelwi.html

[2] Baraka at Imdaadiyyah, 8; Al-Malfoozaat, 4/70, as cited in Ash-Shirk fil-Qadeem wal-Hadith, by Abu Muhammad Zakariya

[3] Al-Istimdaad ala Ajyaal-il-Irtidaad, 32-33, as cited in the aforementioned source

[4] Al-Fatwa Ar-Ridawiyyah, 6/155, as cited in the previous source.

[5] “Oneness of Divine Lordship”