Is it necessary to have firm belief in all the pillars of faith, and in the existence of Allah in particular? What is the meaning of firm belief, and does doubt differ from conjecture regarding the existence of Allah?

Aqeedah (creed) is what the heart firmly believes in without a doubt. It is the firm belief in the six pillars of faith. This includes belief in Allah's existence, His Lordship, His Divinity, and His names and attributes. Doubt in this is not faith. There is a difference between doubt that leads to disbelief and the whisperings that come from Satan's cunning; whisperings are not doubt. The term "dhann" (conjecture) can refer to doubt or certainty, but doubt is of no benefit in matters of aqeedah.