I am wondering about USB 3.0 to HDMI and USB 3.0 to Ethernet RJ45 adapters.

Does it mean even I don't have these connectors (HDMI and RJ45 ETHERNET) on the FPGA SoC / Raspberry Pi boards, I can still use the above mentioned adapters to get HDMI and RJ45 Ethernet through only USB 3.0 port ?

 

Only if you load the respective drivers for each adapter. Some O/S will have built in drivers, others will not...