1) The asthma would be an issue for your AME and FAA aeromedical to address, not the airlines. A past history of asthma as a youth is probably not going to be an issue as long as you do not currently suffer any affects from it. As far as US airlines are concerned, they mostly won't ask or care about past medical issues as long as you have an FAA 1C medical certificate.
2) General consensus in the industry is don't lie about anything. Because if they find out later (they often do) you will be fired immediately, and that will pretty much blacklist you from the entire industry.
3) Airlines will require that you account for any time as an adult when you are not in school or employed (some may only go back ten years). They'll typically want a reliable reference (other than your mom) who can confirm what you were doing during a period of unemployment.
If you tell the truth, this will be something you'll have to explain. IMO it could go either way...
You might be able to convince them that in your youthful enthusiasm to join the military that you made a mistake, learned from it, and will never go there again. You'll need to articulate that you regret doing it because you realize you might have endangered your fellow military personal in a crisis...that is very relevant to aviation medical certification.
Or they might be concerned that you were willing to lie about a medical condition and possibly endanger others just to fulfill your personal desires or needs. Unfortunately, that's a common enough theme in aviation such that any employer will be wary of something like this.
Hard to say which way it will go...the big thing you have going for you is you were young at the time, and people change as they grow up.
But I'm pretty sure you could get a regional job, not so sure about majors.