There does not seem to be much of a history of conditional baptisms in Orthodoxy. The general rule since the council of Trullo in the East has been, following canon 83 of Carthage, to rebaptize anybody whose baptism is in doubt. Certainly the East has always denied, however, that a second baptism for the remission of sins may be provided (so in that sense, the second baptism is implicitly conditional, since it would be held to be ineffectual in the case that the first baptism in doubt was efficacious).
The Orthodox hold, just as the Catholics do, that a baptism cannot be valid unless it is conducted with proper form. The Orthodox differ, however, from the Catholics, in that we reserve the right to invalidate the baptisms of groups outside of the Church essentially for no reason. The understanding is that this comes from the power of the Church to bind and to loose, and so while the Church can cut people off entirely with this power, and declare them to be as heathen (as the seventh canon of the First Council of Constantinople did with the Sabellians), it can also forestall its judgment, and accept the baptisms of groups which have fallen away into heterodoxy (as the First Council of Constantinople did with the Arians).
As for Mormons, their baptisms are not, and have never been, to my knowledge, accepted by the Orthodox.
Thank you for responding to my questions.
God’s peace
micah