Yes. The Rinnegan is not necessary or related to the Susanoo at all. The Rinnegan is completely separated from the Sharingan, with different abilities and different uses.
In Episode 459 of Naruto Shippuden, Sasuke was actually using his Susanoo during the beginning of the fight. However, Sasuke stopped after he realized that Kaguya's Rinne-Sharingan ability could absorb all forms of Jutsu, including his Susanoo.
The reason why he is not using it more often is because of the power scaling. There is no treat right now that can put Sasuke in the position of using the perfect susanoo. The idea of using it against Shin was just to remind people what he can do if he tries harder, but he could have beaten Shin without the Susanoo.
Yes, Amaterasu does still exist as one of his abilities.
The Rinnegan is one of the most powerful dojutsus and has allowed Sasuke to perform some impressive sets of techniques that he can no longer perform. Without the Rinnegan, Sasuke would be much weaker when compared to his best form.
One such element was Madara's EMS ability – the power to reverse time. The animation showed Madara's EMS spinning uncontrollably, resulting in everything moving backwards. This was revealed to be time reversal, a direct ability of his Eternal Mangekyo Sharingan.
In fact, by Part II, Sasuke Uchiha has managed to master the Chidori to the point of not needing a single hand seal to invoke it and could use Fire Release techniques with only one hand seal.
After Obito received his other eye through Madara and replaced it with Rinnegan, the former still couldn't conjure up a Susanoo because Kakashi awakened the other eye in his body. So technically, as he could never awaken both his eyes together in his own body, he wasn't able to activate Susanoo.
Sasuke, on the other hand, lost his Rinnegan after a Momoshiki-possessed Boruto stabbed him in the eye. Considering that it's very unlikely to see Obito come back to life or Kakashi gain the Sharingan again, the only option left to free Naruto is for Sasuke to recover his Rinnegan.
1. Hagoromo Ōtsutsuki. Hagoromo Ōtsutsuki, popularly known as the “Sage of Six Paths,” is the strongest Susanoo user we have seen to date. Rightfully known as the forefather of Shinobi, he had a gigantic Susanoo figure in its complete body form.
To sum it up, in the final developmental stage of a Susanoo, the Perfect Susanoo is stronger than Kurama on its own. However, that does not make it stronger than Kurama in every situation because the Tailed Beast can enhance the jinchuriki's abilities and turn the tables in a battle.
Sasuke's armoured Susanoo (Eternal Mangekyō Sharingan version).
Itachi could use Amaterasu in his right eye. Sasuke has his brother's eyes, which means Sasuke can use Amaterasu in his right eye.
Without Kurama, Naruto lost a big part of what defined his strength, and what also made him who he really is.
In addition to the Rinnegan's power, this eye retains the abilities of Sasuke's left Mangekyō Sharingan, including the ability to cast ocular genjutsu and use Amaterasu.
Way back in Chapter 643, it was noted that by being the ten-tails jinchuriki, Obito can no longer use his Kamui to travel through his pocket dimension nor to become intangible. But in Chapter 674 and 675, Madara was able to use Kamui (by stealing Kakashi's sharingan) despite being a jinchuriki of the ten-tails.
So Obito can transfer any of his body parts that are in contact with the enemy to the time-space of the Kamui and make it look like he cannot be touched.
Though, he can not transport pieces of himself to the other dimension, nor can he touch someone and send them there. Obito could transport himself, and pieces of himself to his dimension. But to transfer others, they have to be within touching range, or actually touching.
The series' protagonist gained a perfect hold over most types of natural Chakra after gaining the Six Path Senjutsu. But the question remains whether he could have mastered Chidori during his teenage days. Well, the answer is no.
If Sasuke had both arms, he may be stronger than he is in Boruto. He can wield hand signs and have more jutsu.
Drawing Hand Signs Became Redundant
The most plausible reason for hand signs becoming less prevalent in the series is the redundancy that came with drawing the same hand seals over and over again for every panel.
Itachi Uchiha
With his left Mangekyō he can use Tsukuyomi, an extremely powerful genjutsu that distorts the victim's perception of time. With his right Mangekyō he can use Amaterasu, creating inextinguishable black flames at the user's focal point. Since he awakened both his Mangekyō, he can use Susanoo.
Despite not being an Uchiha, Kakashi Hatake had a Sharingan, thanks to Obito Uchiha, who gifted it to him in the Third Great Ninja War. In time, he awakened the Mangekyo Sharingan and his strongest ability was Kamui. Using this power, he could warp anything from a distance and send it to the Kamui dimension.
Using his Rinnegan, Madara Uchiha projects a shadow of himself into Limbo (輪墓, Rinbo, Literally meaning: Wheel Grave), an invisible world that coexists with the physical world but that is ordinarily impossible to detect, perceive or even physically interact with.