lol
first of all, everyone has abs.
the reason you cant see urs is, its probably covered by fat.
you should get your body fat measured, and doing a ton of ab workouts wont give u the abs u want, u want to lose the body fat % , and eating right mixed with cardio and resistance training of the whole body!
no getting a 6 pack in less than a month is not a very "logical" set plan man. it takes people months and months to get to that stage, well dependin on ur current stature of course.
judging from ur post, u seem really new, and i do not think u have the body fat % of near 10% or so, that is where your abs start to shine.
pushups dont work ur abs..., dependin on how u do it, if u did pushups on the floor, it would work mostly your upperbody, mainly the chest.
the only time pushups would help the core *ab area* would be when ur trying to do pushups on the swiss *exercise* ball. feet on the ball and do pushups.
pushups in general, does the chest. if u want ab workouts,
crunches
sit ups
bicycles
hanging legraises
roman legraises
these are some examples. there are many