UPDATE: Fionna is Susan Strong who is Finn's mother
The reason I believe Fionna is Susan is because Gumball may be related to Bubblegum (I know it's Gumbald but close enough), so therefore Gumball is like the generation before Bubblegum, therefore leading Fionna is a generation before Finn. Since she is the only female human, she could have married Martin and had Finn. One day, I think Martin ran off with Finn to exchange for something but lost him in the woods. Fionna went franctic, and fell into where the Hyooman tribes live. She then became Susan, but because she maybe fought the Glublub (whatever) she received some serious injury she had to have a transplant...
Anyways, the Lubglub (whatever) that was eating Fionna's hat, may be that her hat fell off and couldn't retrieve it after she got hurt so the tribe gave her the cat hat. The other reason I believe that Susan is Finn's mother is because she sort of remember how to speak English, and when she met Finn she said "sun". Sun sounds like 'son'. Meaning she recognises Finn.
*anyways correct me if I got canon details wrong because my memory is not thay clear and I haven't watched Adventure Time for like a long time so yeah...