1. Are you going to put this hardware in the production environment ? If yes, then you may see performance issue in VM or any other unexpected issue. Reason: VMware always recommend to install the OS in the certified hardware otherwise they wont support for any issue. What is certified hardware? Hardware which is tested and certified by VMware engineering. If it is test environment then you can play around with this hardware. HCL link for hardware
VMware Compatibility Guide: System Search
2. Looks like both the nic card is not supported for the ESX/ESXi which means there is no drivers for this from VMware. ie there is not VMware certified drivers for this hardware. If the vendor(Inter) have drivers available for ESX/ESXi you can use Image Builder software to inject the drivers in the ESXi installation image and proceed installing. But do not expect a good network performance from this network card. look at the below link to know more about Image builder
3. Yes, you can install supported Nic card in the hardware and then try installing ESXi, this should work. Look at the below VMware HCL guide to find the supported network card. Install any of the support Nic card to install ESXi.
VMware Compatibility Guide: I/O Device Search
Let me know if I miss something or if you need more info