In what scenario would they even meet to hatch this plan?
During the Great Galactic War.
Why would she risk creating such a potentially powerful child who could be turned and used against the republic?
She believed she could have the child and teach him alone, Jedi are self confident.
Why would she think that this child would even make a difference in the conflict? I
Jedi believes in heroes and heroes did turn the tide, such as her ancestor Revan, the Exiled and the JK character.
If such a child could make a difference, why not create it with a powerful jedi?
Because other Jedi would not approve such plan and few of them could match Malgus' strength. Also she wanted to let the child become something like Revan, so a little Dark Side is required as well.
Both sides recruit force users. From Malgus's pov, why not do so with a powerful sith?
Because he could not find a female sith who could match Satele's strength, and he didn't trust other Sith. Remember his goal was to become the emperor himself and abolish many stuff. He believed Darth Revan's blood would help him.
Why give Shan such a weapon to raise as a jedi?
He believed he could succeed and he filled the child with the Dark Side of the Force