If I have a hidden Blade hidden at a battlefield, on my opponent's turn can I target my own unit with Blood Money and chain my hidden Blade as a reaction, or do these spells require my unit to die as part of the cost of their abilities?

No — neither spell requires the unit to die as a cost. "Kill a unit at a battlefield" is the effect on both cards, not an additional cost, so the unit is only killed when a spell resolves with a legal target.

On your opponent's turn, Blood Money is Action-speed ("play on your turn or in showdowns"), so you can only play it during a Showdown, not in an open state. If a Showdown is ongoing, yes: play Blood Money on your own 2-Might-or-less unit, then react with your hidden Hidden Blade (it gains Reaction while facedown, Rule 811.6), targeting that same unit — both sit on the chain together. But the chain resolves LIFO: Hidden Blade kills the unit first and you draw 2, then Blood Money's target is gone, so its kill and the "friendly unit" Gold-token instruction are both ignored (Rules 359.3.e.5, 359.3.e.14.a). You can't get both the draw and the Gold tokens from the same unit — only the spell that resolves first gets its kill.