Electronic – Difference between Hirose U.FL and IPEX connectors

From the datasheet it always transmits over one of the antenna connectors and a software algorithm is used to determine the best one at the time to use for receiving:

BCM4312 has 2 radio chains, one is a dedicated Rx chain, the other is shared by TX and RX chain using an RF switch. For RX, It supports antenna diversity and provides four options. A software diversity algorithm is used to determine which option is used.

It doesn't mention what the four options are but in general the idea of using diversity mode is when you think the reception from one antenna is likely to be better than the other, it won't increase range otherwise because only one is actually being used at a time. For further reading here's an article Multipath and Diversity from Cisco that goes into quite a bit of detail on the use cases.

So it's certainly possible to connect a Yagi to each antenna connector and it shouldn't cause any problems as long as you don't use it to try and expand coverage to a wider area. But if it's in a location where multipathing isn't likely to be issue like say outdoors and line-of-sight it won't gain you anything either. In that case you'd be better to spend the extra money on a better antenna and low-loss coax and connectors.

From a practical point of view determining the best setup is mainly a matter of testing various configurations and doing a site survey to make sure all the areas you're interested in have good coverage. The last time I did something similar it was an embedded system that had logging and GPS anyway, but there are a number of phone apps around that may prove useful if the clients will be moving around. For point-to-point you could just measure throughput and reliability over a period of time to make sure it meets your needs.

At resonance the imaginary part is zero, yes. Why is it surprising that there's still a real part?

Imagine a series (or parallel) RLC circuit. At the resonant frequency, the L and C impedance are equal and opposite. But you still have the R.

Another thing - the resistance that's left is not just radiation resistance, some of it is loss resistance - real resistive loss in the wires, etc.