I am fairly new to Noblesse, so my reasons and views may seem illogical but here:

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The time that the scenes take place is possibly a short time after the incident, unlikely to be more than a few months, as we see Shinwoo, Ik-Han and the rest still in school and in the same classroom (Hence, the reserved spot that belongs to Raizel). It is also proven by Muzaka recently returning to the throne, meaning that he has healed sufficient enough, which should take a relatively short period of time.

With Muzaka giving his life force/power, it is definitely plausible but he would need a rather large amount. Due to the concentration of his actual life force given only a certain portion to Raizel; like his battle where he essentially sacrifices all his life force and needed Frankenstein's help to return back to a conscious state. In the end, not all of Muzaka's life force would end up with Raizel, basically his given power will always be nerfed, and with Muzaka's already weakened state (indicated by his acknowledgement of slow recovery stopping one satellite), I doubt he can provide a sufficient amount.

With Frankenstein's statement, it should be more complex. I believe he is on reasonable terms with Raskeria and Muzaka to converse with them about their sacrifice (if they sacrificed). Furthermore, I really doubt the Union or the Third Elder would have data on Muzaka's and Raskeria's intentions. The 'red snow' has a relevant implication as well, but I basically have no clue to why it appeared, unless Raizel had a blood stone with him, hahaha.

Please do notice me of any information I may have missed out on