I heard Aisha (r.a) was engaged before she married Prophet Muhammad (s.a.w). Can you provide details about this? Are they authentic?
Yes, she was engaged to Jubayr ibn Mut'im before she married the prophet (s.a.w).
The idea to match Aisha with Muhammad was suggested by Khawlah bint Hakim. After this, the previous agreement regarding the marriage of Aisha with Jubayr ibn Mut'im was put aside by common consent. -- Wikipedia
Yes al Mut'im ibn 'Aday الْمُطْعِم بْنَ عَدِيّ (he died as a kafir but protected our Prophet from Quraish when he turned back from at-Taa'if and therefore was quoted in a hadith after the battle of Badr) asked abu Bakr for her hand for his son before our Prophet asked Khawla bint Hakim to ask for him.
This is based on this marfo' narration from hadith ibn a-Sammak and al-Khuldi (here the Arabic text), this narration doesn't clearly say which of al-Mut'ims sons was the choosen fiancé!
Abu Bakr asked al-Mut'im soon after the inquirey from our Prophet came and apparently his wife said to abu Bakr something like: "...if we married him to her you might get him convert to your religion...", which abu Bakr understood as an end of the engagement and therefore inivited our Prophet to come to ask for his daughters hand.