Your sentences would probably be understood, but they are not the way fluent speakers would say it.
The straightforward way to ask the first question is, "How many soldiers are in the army?" Or more casually, "How big is the army?"
You could ask, "What is the strength of the army?", but then it's not clear that you're asking for the number of soldiers. Someone might well answer, "Their high morale and training".
There's no clear, concise way to ask the second question. You could get the same idea by asking, "What percentage increase was it?" But then you'd invite the answer, "200%", not "three-fold". You could say, "What factor increase was it?", but that would leave many confused about what you meant. The only way I can think of to get the kind of answer you're looking for would be to ask something wordy, like, "How many times an increase was it? I mean, like was it two-fold, three-fold, four-fold?"
And tangential point, any time someone cites a large increase, it's often unclear whether they mean "percentage that was added" or "percentage of the original number". Like if there used to be 1000 and now there are 3000, I'd say that's 300% of the original number, or a 200% increase. But I have heard people describe that as a 300% increase.
Or just to be crazy, just a couple of days ago I read a news story with the headline, "Crime falls by 87%". The subtitle said that crime in the city where I live fell by 87% last year. That sounded very impressive. But when I read the article, it turned out that what they really meant was that it was now 87% of what it was the year before, that is, it fell by 13%. Still impressive, but nowhere near as impressive as falling by 87%.
