I don't think setting the duplex is a problem. I think the NICs will figure that out on their own. You can plug any ethernet NIC into any other and they will work out the best common supported speed and duplex as well as drop down if the line itself is bad.
This is a negotiated process. I have to assume the link-pulses pass through the diodes, or link wouldn't come up at all. So who knows for sure what will happen to autonegotiation here. I'd think that if there are 3 devices attached, they'll stomp on each other's autoneg bursts, and autoneg just fails. But it's also possible (especially if there's a timing difference as they come up) that autonegotiation succeeds, in which case you will get a full-duplex link. Since there's no provision for re-negotiation once link is up, I'm not sure what happens when the 3rd device comes up. Either link flaps and all 3 redo negotiation (which hopefully fails and you get them all in half-duplex), or more likely IMO only the new device fails autoneg and the other two continue on with their full-duplex link. This will result in undetected collisions and corruption. Either way, it's undefined behaviour.
So disabling autoneg and manually forcing half-duplex is probably necessary for 'reliable' operation. If autoneg fails (as it probably will in a significant proportion of cases), that will result in half-duplex link too, but I wouldn't want to count on that, since I don't think there's anything about this scheme that will cause it to fail reliably.
If not, only one device needs to be set to half duplex and the others will follow.
Normally yes, because autonegotiation will fail, and that will force the NIC to half-duplex. However, in this case, any two of the devices may send FLPs for autonegotiation, so setting only one of them to half-duplex is probably not sufficient as the other two can still negotiate. In fact it might be worse, since you won't have 3 devices competing to autonegotiate any more, which seems like it'd make it more likely to succeed between the other two.
Besides which, this is bad practice. If one side has manual speed/duplex, you should definitely set the other side manually too.
- 100Mb half duplex: NIC driver refused this configuration, maybe not specified by the standard(?)
It's definitely specified and should work. 100base-TX hubs were even a real thing. 1000base-T spec includes half-duplex too, though it isn't a real thing AFAIK. It was finally dropped for 10GBASE-T.