Are they separate layers? Could I use IPFS in my own project, or is it intrinsically tied to Filecoin?

They can. Think of it like a torrent file and a webseed. You can freely use torrents to distribute your content, but if everyone who has ever downloaded it goes offline, any new downloaders will be stuck at 0% forever.

The only add on here is that you can pay some service in filecoin to keep seeding your torrent forever.

Of course you can. There is no substance to this line of reasoning except that PL publishes both.

It's like saying speculating on py-umbral (a standalone open source project) because we use it to build NuCypher (a blockchain-dependent open source project).