我想去电影 is not correct. You can either say: 我想去看电影- I want to go see a movie. or 我想去电影院-I want to go to the movies. 我愿意去电影 means "I am willing to go to the movies." as for "要下雨了" and "会下雨了". Remove 了 and you're good to go. 会下雨 means "[it] will rain" and so does "要下雨." 了 shouldn't be used here， its normally used in a situation where a change is implied i.e. 下雨了-it's raining [now].(it started to rain) 要 doesn't mean the action will happen soon, it's actually the opposite. It means an action will happen later on[not right now] compare the following situations: *you and your friend run into each other on the street* ’你去哪里啊？-where are off to? 我去上班- I'm going to work. Now take a look at this scenario: 暑假快到了，你有什么打算？ (summer vacation's almost here, do you have any plans?) 我要去纽约度假- (I'm going on vacation to New York.) 去多久？= (for how long?) 一个星期=(for one week) Here, 要 means "to be going to" and shows the action is not happening now, but later on. 会 means an action will happen in the future, but isn't necessarily definite compare these scenarios: 下午可能会下雪- it might snow during the afternoon.[this might possibly happen]. 我要送给他一个好吃的生日蛋糕。-I'm going to give him a delicious birthday cake. [this will definitely happen]. 会 can mean something will happen in the future, but isn't necessarily definite, which is why it can be used with 可能(probably) while 要 can't, because it implies the future event will happen.Compare these: 我想去中国- i want to go to China.[but I don't have any money] 我要去中国- I'm going to China [this is definite]

first “去电影”is incorrect in chinese，you should either say 去看电影 or 去电影院 then “我想去看电影”is more for the common future tense，but “我愿意去看电影”is not for the second question，we usually say “要下雨了”when it is a sole judgement if you put a time before it ，it goes like “明天要下雨”or “明天会下雨”they make no much difference

And the difference between: 要下雨了 会下雨了 What is right?? ------------------------------- "要下雨了" means "It is going to rain (soon)." I don't think Chinese use "会下雨了", but "会下雨" means "It is going to rain (but I'm not sure when the rain will come)". "了" usually stands for something already done, or something is coming near. In the first sentence, it gives out the hint of "soon".

愿意：will 想：want

what is the difference between want and would like ??? this is similar to 想 and 愿意 in french, this difference is more clear: je veux quelquechose et je voudrais quelquechose would like 愿意 voudrais are more polite