it is right. if post-positions are added, the sentence is "나는 오늘에 아무것도 안 먹었어요."

i guess so= 나는 그렇게 생각해요. maybe= 아마

"まま"と"ながら"はよく似ているけど、やはり違いがある。 ''まま"の前の動詞は一般的に瞬間動詞である。'まま'はその瞬間動作の結果の残存を表す。本質は一種の状態なのである。 "ながら"の前の動詞は一般的に継続動詞である。"ながら"は前の動作の進行中で後の動作が起こることをあらわす。本質は一種の動作なのである。 靴をはくの"はく"は瞬間動詞であって、'まま'しか使えないのではないかと思っている。

the sentence "그녀에게 돈이 있다" means "she has money." here 에게 doesn't mean to/for. it's a speacial sentence structure.

the independent 지 at the ending means "confirmation", similar to "~~~. right?" e.x. A: 에제 들어왔지?(you came back yeasterday, right?)

는(present tence)/은,ㄴ(past tence) is used for verb. 은,ㄴ(present tence)is use for adjective. there is no past tence for adjective. e.x. 불고기를 먹는 지(if (somebody) eat bulgogi or not) , 불고기를 먹은 지 (if (somebody) ate bulgogi or not).

귀여워 has no special meaning. 귀여운데 includes the meaning "but". e.x. A: 이 고양이가 섫어 (i don't like that cat). B:그래, 귀여운데.(really? but i find it so cute). 귀엽네 has the meaning of admiration. 이 고양이는 귀엽네 (oh, how cute the cat is!) all the three forms above is impolite form. if they are added with 요, they are transformed to polite form. 귀여워-귀여워요 귀여운데-귀여운데요 귀엽네-귀엽네요.

first i should say there are two system in korean. 1 polite speech 2 impolite speech. easily speaking "impolite form + 요 = polite form". e.x. 좋아-좋아요(good) 좋은데-좋은데요. so in order to solve the problem in the same level, we should discuss the difference between "귀여운데 and 귀여워" .