I have an '81 FI spider too.
It is a little hard to tell from your photos, but I think you might be missing the entire bracket that holds both the filter and the fuel pump (in a line). It also looks like they are in the wrong order (if I see the photo correctly). The line should come from the tank, go into the pump
first, and then into the filter, then up to the engine compartment. I know, it seems wierd, but that is the correct order.
Edit: No, I change my mind; the order looks correct, now that I look more closely at the photos.
Another edit: I think I see part of the original bracket just above the pump in the first pic. So if you get the correct pump, it should mount onto that bracket, much like the filter does. A short and straight piece of hose connects the two items.
The filter looks stock. It's cheap to replace. Get one. The pump (which looks like it is not mounted to anything in your photo) might be an okay substitute. If you are not having fuel issues, then it is probably okay. If it has make and model number on it, look it up online and see if it has the volume and pressure you need. I've found that many pumps will work fine. I have four different bosch pumps and they all produce enough volume and pressure. If you look hard, there are some bosch pump tables that show the various specs.
Edit: your pump is very small - almost half the size of a stock (bosch) pump. Probably puts out less than needed.
I suspect you also might have a kink in that hose between the pump and filter. But that will go away when you rectify things.
Ideally, you should buy a replacement pump (search this forum for advice - people have bought good ones, new, under $100). Absolutely, buy a new (proper) filter, and also try to get a bracket. If you can't get a bracket (used), you can fabricate something quite easily. Someone might have a photo handy, or I could take one. It is a simple setup.
You don't like those connectors?

You won't want to see mine!