How to get a flat stomach/abs & lose weight in an apartment?

So i’ve been trying to lose weight and get a flatter stomach/abs for quite a while now.. i try to do crunches & situps, but i pretty much suck…i live in an apartment so it’s kinda small, and we have a "gym" but i get really self concious..

SOO what can i do IN (key word..IN) my apartment (with no stairs) to lose some weight (besides running around) and get a flatter stomach?

BTW, i am a vegetarian, so no meat/fish/poultry..but i tend to splurge on the carbs and sugar, to fill me up.. any diet plans/ideas? (i’ve been drinking alot of water lately too)
oh yeah, and on my tummy, i have that little curve under my belly – i dont know if its extra skin or fat or whatever, but i KNOW its get-rid-able

so how do i get rid of that?!