Like Jon said, for "What do you wanna eat?" you can use "뭐 먹고 싶어?" or "뭐 먹을래?" Both those expressions are correct. For "Let's go watch a movie!", if you really want to include the "go," then you can say "영화 보러 가자." When you're going or coming in order to do something, you can use the pattern 'verb stem + (으)러 + motion verb': Let's go see a movie: 영화 보러 가자. Let's go eat: 밥 먹으러 가자. For "I'm watching TV" you can say "지금 TV를 보고 있어." You can form the present progressive by using the pattern 'verb stem + 고 있다'. All these expressions are informal. To make the polite versions, you can change them like this: -을래/ㄹ래 -> 을래요/ㄹ래요 (note that this verb ending, like '-고 싶다' is only used for first person statements and second person questions). -자 -> -ㅂ시다/읍시다 (note that there no '-요' form of this verb ending, nor for ㄴ다/는다, (느)냐, or, (으)라). -어/아 -> -어요/아요.

I'm still a newbie at korean but i will guess just to practice, then natives can correct me. ^^ What do you wanna eat? 뭐 먹고 싶어? or 뭐 먹을래? - i think this is more common Let's go watch a movie! 영화 보자! - More like.. let's watch a movie. Not sure about the last one.