Some of these I can't even fathom what they are used for.
I"m going out on a limb and risk the engineers hammer is the tool used when everything else has already failed to separate, combine, detache, attache, couple, decouple, split or join.
Engineers hammer is used to smack things and see what happens. You're not meant to drive nails or shape metal with it, but it's used to do inspections.
For example, a structural engineer inspecting a truss bridge might go and smack every stringer or strut near the rivet to the beam to see what happens. If the strut jiggles a bit, then the rivet has loosened and might need to be replaced.
If a bit of steel is heavily rusted, the engie might belt it really hard to see if it breaks due to deep corrosion, or if it's just surface rust.
The sound you get from smacking a bit of steel can also tell you about the material, good steel will bong and reverb, bad steel will be dull and not reverb.
TIL that finishing a shaped metal sheet by pounding it on a pedestal is called "planishing" and said pedestal is called a "planishing stake." I've seen it done I just never thought to ask what it was called, I guess.
I'm what the aerospace industry calls a "surface enhancement engineer." A fancy way of calling me a peener. I mostly work with CNC air blast shot peening machines but the principle is essentially the same as a ball peen hammer.
Basically, hitting metal with hard ball causes little dimples to form on the surface of your work piece. Hit it a shit load of times and you get dimples all over. At the end of the day all those dimples help prevent stress fractures from forming.
Soft face is exactly what it says, it's got soft rubber faces, basically just a shrunk down rubber mallet. Use it on things you don't want to leave marks on.
Double peen is basically just a soft face except one side is like a hard epoxy like material. Harder than the rubber side, still softer than a metal head would be.
Fun hammer fact: it's called dead blow not because it's supremely powerful or anything, but because the head is usually full of loose material like BBs, and it causes the hammer to not bounce back as much, kinda like throwing a hackey sack at the floor