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 :)