With a sentence like this I would be extremely surprised if kroppen was still a living being. You wouldn't refer to something/one alive as just a body. So this is indeed one of the few instances where kropp does mean "body", as in a corpse.
Oftentimes kropp is used as an euphemism for the harsher term of lik, but they are not necessarily interchangeable terms.
I watched two animated versions and on, "Jeg har kroppen full," (version 1, Barnesanger på norsk), the lamb is suddenly in a big sack and, in version 2 (Barnesang for barn og de minste Tinyschool Norsk) it shows three sacks (consistent with the English version). So, natural mistake. I'm glad you explained. :0)
I've included both links.
Yes, "lillebror" is "baby/little/younger brother", and anything being referred to as "bitte lite" is very small or tiny, itty-bitty even. That makes "baby brother" the most appropriate of the three, and you could even go with "little baby brother".
"Bitte" functions as an intensifier, like "kjempe-", but only works in combination with the adjective "liten", and is an adverb rather than a prefix. When someone asks for "bitte litt" of something, they only want a little bit, so that's easy to remember.
"Lik" is interesting to me. It seems that most Germanic languages have a word that's similar to this, but I can't seem to recall there being any English cognate. That being said, it does sound a bit like "lich," a word really only known to fans of like, old-school RPGs (e.g.: Ogre Battle, Final Fantasy [I think xP] etc.) Tror du det kan være en forbindelse? (Apologies if that's incorrect.)
Lich IS the English cognate, it's just more associated with fantasy when it was revived after it fell out of use in middle/early modern English when French 'corpse' became more trendy.
Lich is also the origin of 'like' (by which its form is pleasing), as well as -ly endings in adverbs (gladly = Old English 'glædlíce' i.e. glad-like).
It's things like that which make the original word overlooked such as a 'wight' (a creature or thing), which forms the basis of 'aught/owt' (áwíht, a wight), 'naught/nowt/not' (náwíht>náht, no wight), literally 'a thing' and 'no thing'.
"Gulvet" is the bottom of the inside of a room/cube/box, ie floor. "Bakken" is the earth, soil, ground.
Erecting a tent on the ground transfers that piece of soil with some cloth on it into a floor. If your tent is the tall kind I think is called a party tent, it has no floor, as there is only walls and a roof included in the build.