Do all mantras that gives siddhi needs guru initiation? Or are there any mantras that can give siddhi without the need of guru?
Yes, except the mantras like "Hare Rama, Hare Krishna" or "Om Namo Narayana" given by saints like Chaitnaya Mahaprabhu, Ramanujacharya to entire mankind, all other mantras need initiation, even if they are simple Gayatri Mantra or "Om".
D: “Can anyone get any benefit by repeating sacred syllables (mantras) picked up casually?
M.: “No. He must be competent and initiated in such mantras.” Maharshi illustrated this by the following story: A King visited his Premier in his residence. There he was told that the Premier was engaged in repetition of sacred syllables. The King waited for him and, on meeting him, asked what the words were. The Premier said that it was the holiest of all, Gayatri. The King desired to be initiated by the Premier. But the Premier confessed his inability to initiate him. Therefore the King learned it from someone else, and meeting the Minister later he repeated the Gayatri and wanted to know if it was right. The Minister said that the mantra was correct, but it was not proper for him to say it. When pressed for an explanation, the Minister called to a page close by and ordered him to take hold of the King. The order was not obeyed. The order was often repeated, and still not obeyed. The King flew into a rage and ordered the same man to hold the Minister, and it was immediately done. The Minister laughed and said that the incident was the explanation required by the King. “How?” asked the King. The Minister replied, “The order was the same and the executor also, but the authority was different. When I ordered, the effect was nil, whereas, when you ordered, there was immediate effect. Similarly with mantras.”