1.没问题；2：应该是Can you go out with me?情态动词后要加动词原型,所以,3句中应该是You can watch TV.
going to可接动词原型,如I am going to play football .
或地点名词（此时going to中的go是实义动词）,如I am going to school soon.
;going for 后可接名词或ing形式的动词,如I am going for a walk；playing前应该有个be动词的,后面接名词或名词词组,如
I am playing football now.