I am wondering what new chapters are in Rites of Battle?

Imperial Fists. In addition there is a sizable amount of introduction to Successor Chapters of:

Ultramarines: Novamarines, White Consuls, Black Consuls, Mortificators, Genisis Chapter

Dark Angels: Consecrators, Angels of Redemption, Angels of Absolution

Blood Angels: Flesh Tearers,Lmenters, Blood Drinkers, Knights of Blood

Imperial Fists: Crimson Fists, Hammers of Dorn, Subjugators

Thre is also a section on Custom Chapter Creation. I haven't gotten a chance for a dtailed reading through just yet. I've provided the above info from the Table of Contents.

So, all of the successor chapters were created by members of the main chapter. Do the successor chapters have Primarchs or were there only the original 13?

My history is a little off.

No: Successor Chapters do not have Primarchs. They are 'spin offs' that used the geneseed of their original Chapter. It was originally 20 Primarchs, but 2 were deleted from history, and 9 (was it?) turned traitor.

All chapters would venerate the Primarch of their original chapter to some extent, if they know who their parent chapter was.

The second founding chapters are just the legions broken up. Second founding chapters would have just as strong ties to their Primarch as any first founding chapter. Third founding chapters and any chapter founded later would more likely have less and less focus on Primarch as they get further and further away from the time of the Primarchs.