As to where the Geneseed comes from, it depends on how and when the Chapter is being founded. There are basically two ways for a new Chapter to be founded; directly by a parent Chapter, or at the order of the High Lords of Terra from the Adeptus Mechanicus and Inquisition Geneseed stores. The former happens when a Chapter has enough neophytes and Marines that it's exceeding the Codex organization and enough Geneseed stores for rapid recruitment, all in-house. In this case, the Geneseed all comes from that Chapter's pool, and would be considered a Successor to that Chapter directly, and to that Chapter's First Founding Legion indirectly. So, if the Crimson Fists had an excess of Marines (not that they do), they might Found a new Successor Chapter, who would be considered Crimson Fists Successors first, Imperial Fists Successors roughly equally and spiritual followers of Dorn.

The other route, as exemplified with the Cursed Foundings, uses Geneseed from only the Inquisition and Mechanicus knows where, with Chapters that mostly don't even know which Primarch their Gene-stock comes from, with rumours that leftover Geneseed from Traitor Legions was used for, say, the Minotaurs (I think).

In practice, there are already two Black Templars Successors (probably), the White and Red Templars, though the Whites are unconfirmed because the BT don't exactly share much with the rest of the Imperium. At least the Red Templars were merely a gesture to appease the Inquisition and attempt to look like a Codex chapter. In short, there's nothing preventing you from having a Successor to whatever Chapter you want, as long as it's not a Cursed Founding Chapter.