Is it possible that I install VMware ESXI on new HDD through my laptop, then plug that HDD to my server computer.
I mean will there be any driver issue or hardware change issue after I plug it in server
I don't even understand why you would want to do this. Even if it would work, it would be 10x more complex than simply configuring the server using the ESXi installer.
I'm pretty sure it will, most of laptops are not supported by default and you have to manually add drivers.
If your server is not supported on VMware compatibility matrix the situation might be the same.
Use ESXi installer, is not that hard, If you need any assistance you can reach me.