No, this card is PCI, not PCIe

No, this is not possible. But you can use PCIe x1 or PCIe x4 cards in a PCIe x16 slot if you don't have any additional slots. Here is a suitable product: TP-LINK TL-WN881ND (PCI-E x1, 300Mbit/s)

Apparently yes, I connected this card to a 5-6 year old desktop PC and no problem.
PCIe 3 was introduced in 2004 and PCI 4 replaced it in 2017, so in principle "No Problem"