When you make very delicious food and you want your roomie to know its taste, but you don't want to share it as you are hungry too, do you say "take a bite"?
Sure. Take a bite, means have one bite. It does not explicitly say, don't take two bites, but sort of implied in your scenario.
Can also be used for someone not wanting to try something new. Take abite. You will like it.
2) go to my flat - flat here usually refers to apartment or house?
Yes. Regional use, I presume. Very common here in New Zealand. We don't use "roomie". We don;t share rooms, but flats, so it is "flatmate".
3)what do standard-issue and government-issue mean?
Standard issue - well, normal.
A: Are these the normal ones everyone gets or something special?
B: Yes, those are standard issue. Everyone is given the same type.
"issue" means given, here. Not that everyone buys the same sort.
Government issue - the government is the issuing body. The type given by the government.
A: Wow, are those boots legit service boots.
B: Yep, government issue. The real McCoy.