I guess u mixed it wrongly, DDM is calculated based on the GGM if dividend grow in perpetuity in the terminal years. There is 2 different GGM in CFA level 2, one is for calculating the ERP and one is for DDM.
You’re correct about the GGM. Even if you try and calculate it you get a negative number. R must always > g. You’re correct again. The last stage is the perpetual growth part where once again like with GGM you have to have r > g. For the stages with the g > r you only use the growth rate to grow the dividends until you reach your steady growth rate in perpetuity. R is only used to discount the divs and in the TV perpetuity calculation so a g > r doesn’t matter anywhere else.