Yes, but I would encourage you to refrain from using romanization as soon as you can. It will help you in the long term ;)
Is it a composite word, as in 영 means one thing and 화 another? Like "moving"+"picture"?
Yes exactly. This is often the case for Hanja based words (Chinese origin) and if you have the time/motivation to learn those, it may help you guess the meaning of future words. Note that that is not a requirement anymore in the curriculum of Korean kids. So, up to you if you think it is worth it. Not all course creators agree on this issue, from what I've heard.
영국: movie theater (국 means place if I remember well)
화면: screen (picture + face/side, if I remember well)
if a movie theater is 영국 , and what is England then? , how do you say movie theater in England?
映 (영) means “reflection” or “projection”. 畫 (화) means “drawing” or “picture”.
This is not the Chinese term for “movie”, but it certainly makes sense in its own right. Because I know Chinese, looking up (on www.wiktionary.com) the origins of Sino-Korean words is not only interesting but also helpful to me for remembering the Korean vocabulary.