In "Former Master", it doesn't explain how Ryouma managed to get way from the Retrograde Tantou, but it's possible that his bodyguard protected him and bought some time for him to escape. We see that Ryouma's bodyguard received a shallow wound on his head already, so one can piece together that he might have fought the Retrograde Tantou and managed to defeat it, but at the cost of getting injured.
In "Iron Law", The reason why Sakamoto Ryoma and his companions left the Satsuma residence early, instead of departing in two weeks time as recorded was because history was starting to slowly change due to the instability of time-space. It's a good thing though, since the Retrograde Army burned down the Satsuma residence later that night, thinking Ryoma was still inside. Had Ryoma not left earlier on, he would have been killed by the Retrograde Army along with his companions.
In the second episode, it makes sense why the Saniwa has to return to the Citadel since their hand was seen briefly fading away. Since they use a form of Mental Time Travel, they can't expend all of their energy in one place. Had they not returned to the Citadel, the Saniwa will either fade out of existence or suffer a worse fate.
In the seventh episode, the abnormal "Street Slasher" Retrograde naginata might be Ashikaga Yoshiteru's spirit born from revenge and blood lust. It's a possibility since Ashikage's spirit refuses to accept death and turns into a new type History Retrograde that can summon other type Retrograde soldiers similar how the Saniwa can summon the Touken Danshi.
In the ninth episode, before safely returning Ryoma to the Satsuma residence, Mutsunokami for a moment plays with the idea of running away with Ryoma by going somewhere far away with him. Judging by his tone, he seems to want to take his former master to a place where nobody recognizes him, so that he can protect him and always be by his side as deep down, he truly doesn't want to lose him again. Had he not changed his mind however, he would not only be changing history, but he would also be betraying the Saniwa and the rest of the Touken Danshi in the process, making him no better than the History Retrograde Force.
Horikawa is leaning towards that same idea as Mutsunokami in the tenth episode. And the eleventh episode more or less confirms this. Luckily, it only takes a bit of convincing to keep him from changing anything.
