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.