There are two forms of enlistment: volunteer and forced.
To avoid volunteer enlistment, simply don't enlist - you need to sign a form and make the application, so just don't do it. Free and simple.
Forced enlistment, or conscription or military service, is unavoidable. If you have been selected, you have to do it (pending medical or conscience reasons). Paying people to let you off the hook is tantamount to bribery, and illegal.
"Bounty Jumpers".
deserters
There is no more mandatory enlistment. It was removed by the "Bundestag" in 2011.
The US Army has an enlistment program to help recruit troops.
While I am not certain why you would lie to get out of enlistment into a volunteer Army, I do know that any falsehoods you gave on enlistment papers can bar you from enlistment or if enlisted could be grounds for removal from the Army, and potentially prosecution. If you lied to avoid enlistment for some reason, it would be best to reflect on those reasons and determine if those reasons have been resolved. Once you enlist, you are committed for that enlistment period, there is no turning back, so to speak. Be certain that serving is what you want. Do not make the commitment unless you are unquestionably certain.
enlist or enlistment
A standard term of enlistment in the US Army in 1964 was 2 years. Source: My dad, who was enlisted for 2 years.
bounties
When his enlistment term is up, or when he is discharged.
In the US Army, no. The minimum age for enlistment in the US military is 17.
ages 17-49 Mandatory Male Enlistment Age (for the populations subject to mandatory enlistment): 17-21 Mandatory Female Enlistment Age (for the populations subject to mandatory enlistment): 17-20
Typically you'll receive the second half after your 3 year enlistment anniversary.