Why dose the SA not have Baptism? Is the SA a Young earth Creationist Org or do they allow other views of the Genisis account.
I think that a major reason is that some have given the ceremonies (sacraments) a significance higher than they deserve. The Army believes that their function is to draw attention to the truths they symbolise, and to stimulate those who use them to commit themselves to Christ.
For example, some regard them as being the means by which the inward work of grace is communicated, as though being baptised in water has an efficacy of themselves. It was initially an act of public confession and a committal to fulfil the demands of Christian discipleship, but some have twisted the act of baptism to being important in
receiving salvation.
I think that the Army has the stance it does to avoid this kind of erroneous beliefs that twist the purpose of the sacraments. In a sense, it avoids the temptation to introduce other non-Scriptural rules, for example, the Charismatic/Pentecostal movement places a high importance on speaking in tongues as evidence that one has the Holy Spirit - something that isn't even in the Bible! When your theology gets that bad, what good are you? How can you be used by God to teach truth to someone else when you wouldn't know what it was if it did a lap-dance on you?
All of that said, some of the [Army] churches (maybe most) do have communion occasionally and do baptisms (at request), amongst other things. They just keep them in focus and proper purpose.
As for the other question, the Army doesn't have an exhaustive list of doctrines, but only 11 that summarise their core beliefs, which is both its strength and weakness.The
Handbook of Doctrine tries to expound on these core beliefs. It talks about God creating our first parents (Adam and Eve) in a state of innocence, that they fell, and became sinners. I'll let you draw your own conclusions from that. They don't explicitly say one way or the other, but I think it's logical to conclude that if they believe the things stated above, then they should believe the rest, but who knows? To be honest though, hardly any sermons that I have heard even mention Genesis.
To be specific:
[2] a. Whether the Genesis account is taken literally or as a revelation in parable form of eternal truth, the story of the Fall teaches certain undeniable truths of life and history:
i. All men share a common parentage.
ii. Man is not as he was created.
iii. Man has been exposed and has yielded to temptation from the beginning of history, with unhappy results for himself and his posterity.
To me anyway, the above makes little sense, logically, but that's for another time I guess.
One thing that disturbed me as I was reading through bits and pieces of it was that it didn't make any real note of death as a punishment of sin, neither in that section or in the section about Christ's death. Strange, considering that it is at the core of Christian belief for the cross to mean anything and make any sense...

Sigh, I guess no church denomination has entirely good doctrine.