I'll tell let you know exact meaning and usage of them. 1. +랑/이랑, +와/과 and +하고 They mean "and" between nouns. +랑/이랑 and +하고 are spoken. and +와/과 is written. It's up to you. 친구랑 나랑 저녁을 먹었다. - Friend and I ate dinner. 피자하고 샌드위치를 먹었다. - I ate a pizza and a sandwich. 나는 고양이와 강아지를 좋아한다. - I like a kitten and a puppy. 2. +은/는, +이/가 and +을/를 +은/는 and +이/가 are for a subject. Usually, Korean people use +은/는 but if you want to make a point, then you can use +이/가. Actually, in real life, we don't assort thoes. But the usage's difference is like that. Therefore, it's up to you 나는 미국 사람이다. - I am an American. 내가 미국 사람이다. - I am the American. +을/를 is for an object. That's easy to understnad I guess. 나는 콜라를 좋아한다. - I like coke. 3. +하고 있다 and +한다 They are Korean present continous tense. the basic form is +하고 있다. And +한다 is abbriviation of +하고 있다. So they have same meaning. The interesting thing is that +해 is abbriviation of +한다. 나는 숙제를 하고 있다. - I am doing homework. 나는 숙제를 한다. - I'm doing homework. 나는 숙제 해. - I'm doing homework. Plus, if you want to use order form, then you can use +해 with "!". 숙제 해! - Do your homeowork! I hope my explanation will be helpful to you :)

To add on to the other answers, In almost everywehre I've seen that teches korean says that even though (이)랑 and 하고 both translate to 'and' between nouns, (이)랑) can also be translated as 'with' ex. 나는 친구랑 먹어요. I eat with my friend. Heres a good video that really explains the "and"s and the "with"s: https://www.youtube.com/watch?v=NntcJfJN3R4