Is the sentence "beyond a shadow of a doubt" correct and natural to say in English? Example: I believe, beyond a shadow of a doubt, that she is innocent. Thanks in advance!

Is it correct? Another way to say that? A couple of the bands that I really like are/were (...)

First day studying Spanish.. Could you correct me? Hola, Me llamo Raphael.. Soy brasileño y hoy és mi primer dia estudiando español. Na verdad, estaba estudiando inglés y japones al miesmo tiempo. Pero yo voy estudiar español porque para mi és más importante ahora.. Un dia yo quiero voltar a estudiar japones.. Muchas gracias !! :)

What's the meaning of this sentence? "You want to get mad at me, don't you?"

Are these sentences correct? The weather couldn't have been better to study languages. The weather couldn't have been better to know new people in the world, thanks to the Italki. (Could I use the word "weather" related with "circumstances, life situations, etc.."?)

What's the meaning of this sentence? "You gotta be able to smile through the bullshit."

What's the difference between "glass" and "cup"? For example: --> a glass of water; --> a cup of water.

What's the difference between "outta" and "out"? For example: I gotta get out of here. I gotta get outta here.

What's the difference between these sentences I gave up on you. I give up on you. i've given up on you.