There should be ‘to’ before ‘see’ : ‘Let’s go to see the fireworks’. In American colloquial speaking the ‘to’ is often omitted.

Because in your examples you have not given a 'place' that you are 'going to'. You can go to the shop, but not *go to the shopping". Shopping is an activity not a place.

Hey Mohammed The word “to” would be used to show a place where we are going! “I am going to school.” “Let’s go to the park.” “When will we go to the beach.” See how all those are places and all use “to.” On the other hand, we can just use “go” to show WHAT we will do. “Let’s go see the fireworks.” “I’ll go shopping today.” If the sentence answers “what will you do” then you can just use “go” on its own! Hope these tips help :)