You could say those sentence with or without 'up'. The 'up' isn't necessary. You could also say 'Fasten your seatbelt' or 'Do your seat belt up'. Fasten and do up are more useful than 'buckle' because they can be used in more contexts. Note that the sign in aeroplanes usually says 'Fasten your seatbelts'. We don't usually say either 'ground' or 'chopped' with steak. In US English it's ground beef, and in the UK it's minced beef or just 'mince'.

Bonjour Joffrey! In the US, I would say that either phrase is fine. I think "Buckle your belt" / "Unbuckle your belt" are probably more common, though. And just an additional note - if I were to hear the phrase "Buckle Up" (without immediate context) I would automatically think of seatbelts in a car. I think you may mean "ground beef." Are you asking about the ground meat used for making hamburgers, etc?