A 1030 will only use x4 of the PCIe lanes - it can physically fit a x16 slot, yes.
As for the dated system, the Gen1 shouldn't be an issue alone, but you may well have some BIOS/UEFI related errors in getting the 1030 to work.
Which motherboard do you have? I'd search for the motherboard and see if anybody has a 900 series (or 10 series) card working with it.