I'm a little unclear on this phrase's meaning. Does it describe the state of a swimmer jumping headlong into a pool, for example? Do you need to use instrumental case 'с головой (with your head)', not genitive case 'с/из/от головы (from your head)'?
It means to "to go under water completely" and de-facto is used sometimes not only for human beings but for inanimate objects as well (you can google for instance "Забайкалье с головой уходит под воду") - but that would be a mistake. So yes, it has quite a literal meaning - to go under water with head [covered with water] and yes, it's with instrumental case.
There's one related idiom it worth to know about -
уйти с головой (dedicate you completely to something) - like in
уйти с головой в работу.
As of usages you've mentioned:
С головыis "starting from the head", like in "рыба гниёт с головы".
Из головыstands for "out of head", like in "никак не выкинуть её из головы".
От головыis "from head", like in "от головы до шеи".
For diver - an intended action - it would usually be "submerge", "погрузиться с головой".
The "уйти с головой" idiom has a tint of something unexpected happening.
Like a child after rain was running in the street, splashing the puddles, but one so pretty puddle only seemed small but was actually deep, and the kid suddenly "went down all way with his head". Or a car falling from a bridge due to driver's mishap. Or a winter ice over a river suddenly cracking behind you while you believed it is thick and solid all the way.
It is not always so, for example "уйти с головой в работу" is about purposely tuning out the world around you, not some strange occurrence. But in many enough use cases this tint would be present, so be aware.
I guess (not knowing the context) in this case it has a very simple meaning like “to dive/ go under water completely” - first your legs, then body with arms and only then your head.”
In case you use с головой в работу then it has a little bit different meaning like “to dedicate yourself to the work completely” it has a parallel with diving...