With twisted pair and a repeater hub, the hub is not much more than a
digital amplifier. For that it senses a carrier from an incoming signal
on one port and switches all other ports to output mode. In this output
mode, any additional incoming carrier is a collision. This triggers a
jam signal to propagate the collision and make the sender stop
transmitting.
This repeating method mimicks the behavior of the previous, shared
media Ethernet variants (10BASE5 & 10BASE2) where repeater were only
used as physical segment joints or line extenders. Of course you're
correct: twisted pair is a full duplex medium on the wire level where a
collision only happens on the upper physical layer and not on the wire
itself.
A repeater cannot permit more than one sender at the same time.
Multiple simultaneous transmissions would mix on the output ports and
produce unintelligible noise. Likewise, any node in half-duplex mode
assumes a shared medium, incapable of full-duplex transmission. Any
carrier sensed while transmitting is a collision, causing the sender to
back off. Whether the medium is full-duplex capable (fiber, twisted
pair) or not (coax) doesn't matter.
With a duplex mismatch, one link end is in half-duplex mode and the
other in full-duplex mode. Now, when the half-duplex (HDX) side is
transmitting, any carrier on its receiver causes a collision to be
detected. However, the full-duplex (FDX) side may be happily sending
away while it is receiving from the HDX side and it is completely
oblivious to the collisions that it creates on the far side. The HDX
side needs to abort the transmission and sends a jam signal. Since the
FDX side cannot detect the alleged collision it detects a partial and
therefore damaged frame.
Low-frequency and small frames have a reasonable chance to get through this duplex mismatch, so a ping
could actually work. However, as soon as any serious transmission is
trying to get under way, the higher frame frequency and larger size will
make the transmissions fail very reliably.
With unmanaged switches, a duplex mismatch can be very hard to
detect, especially when not even the host NICs report their duplex mode
properly.
With managed switches, you usually have port error counters.
Increasing collisions on one side (HDX) and increasing runts and FCS
errors on the other side (FDX) are very strong indications for a duplex
mismatch.
Basically, relying on Auto Negotiation is a very good practice to
avoid duplex mismatches. Manually configuring speed and duplex mode is
generally prone to creating a mismatch, especially when replacing
equipment a few years later on. Fortunately the whole half-duplex scheme
went away with Gigabit Ethernet and faster.