Black Zetsu stated that Hagoromo awakened the Rinnegan. It's important to understand that awakening and inheriting are too different concepts. This would lead to us believing Hagoromo only inherited his mother's Chakra and he adapted his own power later on - Rinnegan and Six Paths Senjutsu. Hamura had created the Tenseigan despite the latter being an almost identical to the Six Paths Senjutsu. Rinne Sharingan maybe an origin to the Rinnegan and Sharingan, but has different design and powers than them. So the answer is she cannot use any Rinnegan or Sharingan Jutsu, but can only use the Jutsu of the Rinne Sharingan.
As for Hagoromo and Susanoo; yes he has it. Sasuke got the same PS as Indra had from Hagoromo's Chakra, who Indra had also inherited to use the same PS.
