This type of injury is referred to as “Barotrauma” https://en.wikipedia.org/wiki/Barotrauma . The bruising is caused by rupture of capillaries and small veins. Normal capillary pressure is 0.19-0.44 psi above ambient, but this becomes 30x higher when a body part is exposed to hard vacuum. This results in rupture of capillaries (a Hickie) but also leakage of plasma from the intravascular space into the extravascular space. Swelling, in other words.
The situation is even worse in venules (small veins ) because they are larger in diameter than capillaries, so higher wall stress is developed.
The specific situation you describe, where a finger is poked through a sealed hole between the 14psi ISS and hard vacuum, is very bad news. The swelling would rapidly cut off arterial blood flow (2.32 psi) to the finger. The finger dies, turns black and falls off a few weeks later. This is called Ring Tourniquet Syndrome when caused by jewelry rings https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6581218
The amount of permanent injury depends on the duration of interrupted blood flow (called ischemia) and the temperature of the ischemic body part. One series https://pubmed.ncbi.nlm.nih.gov/20179474 reviewed 25 fingers which had been severed and surgically re-implanted more than 24 hours later. They had a 64% “success” rate. “Success” meant the reimplanted fingers stayed pink instead of falling off. They didn’t necessarily work very well. Stiff, non-functional fingers are a big enough nuisance that patients sometimes request to have them amputated.
So, to answer your questions:
If the hole was the diameter of his finger tip, more damage would
have resulted.
If you stuck an entire finger through a hole, the finger would be
damaged up to the hull line. After a few minutes, the finger would
swell to the point where it could not be retrieved. The only
realistic action would be to cut the finger off flush with the hull.
Then put a patch on the hole... which is what should have been done in
the first place. A finger-sized hole in the ISS is a pretty relaxed
emergency. There is plenty of time to reach for the patch kit.
One emergency room maneuver for treating "Ring Tourniquet Syndrome is to wrap the finger (from distal to proximal) with string. This compresses the swollen tissue, gradually squeezing the fluid back past the ring. While this may work in theory, it doesn't work well in an ER and would be even less practical done as an EVA.
The severed finger would likely shoot out of the hole into space (like a pop-gun) due to the 14psi atmosphere in the ISS. Orbital mechanics would return it to the ISS one orbit later. So, if you could arrange an emergency EVA with a catcher's mitt, the finger could be retrieved.
Note: the Little Dutch Boy got away with his antics because the pressure in the hole was positive, not a vacuum.
