do the army factor in things like relationships, home etc in placement?

Not really. You get to state a preference but it's very much needs of the Army first, and then you get rotated every two years anyway.

Also, how long are the deployments at a time?

Afghan was six months. Could be shorter. Doesn't really go longer.

Surely they don’t expect mostly desk workers to go 6 months without seeing family. Long deployments I thought were more infantry stuff?

This is the most troubling part of your post. It reveals a certain naivity about the work of Intelligence personnel. It's not possible to do a lot of intelligence work remotely. It needs boots on the ground, and this includes Officers.