No. The adjective is correct.
"the amount of time that young people spend inactive."
means "the amount of time that young people spend as a result of being inactive."
This use of adjectives has two categories:
I shot him dead = I shot him [and, as a result, he was] dead.
No, "inactively" doesn't work here. This is what the relative clause says:
Young people spend X amount of time inactive.
Which could be read along these lines:
Young people are inactive for X hours a day on average.
The adjective "inactive" says something about the subject "young people".
The problem is the two meanings of "funnily"
OED: Funnily 1: In an amusing or humorous manner; comically.
1929 Manitoba Free Press 19 Nov. 19/2 [The play] is produced against settings that are very graceful. Starts funnily and ends more funnily.
OED: Funnily 2. Strangely, oddly, curiously; surprisingly. Also frequently as a sentence adverb. ...
It is correct, but I doubt it is formal. You know, the online dictionaries love to explain adverbs in a format like this "in a [adjective] way". So, why not try to replace it in your sentence and it can be read as "B is also assumed but in an implicit way", which sounds totally fine.
The sentence does have problems but I am not sure that "additionally" is the significant one. In your sentence, "additionally" is a free modifier that fronts the clause, "conducted a lot of well-organized sports clubs." As, for example, in "Unfortunately, you have lost."
Fronting free modifiers are usually offset with a comma or commas.
In short, I would ...
Ago works well here. It retains some of the nuance of time and can only really be replaced by "earlier" - which would refer to earlier in my journey which is neutral as to whether it means "at an earlier point", or "at an earlier time."
"Funnily enough, I do believe in democracy". [my sentence]
"Funnily enough, he did say he believed in democracy". [my sentence]
funnily enough is an idiomatic expression that means that what you say after it is unexpected. It can be placed at the beginning or at the end of a sentence, and not usually in the middle. It is more spoken than written. It is ...