“Beside” VS “Next to” VS “By”

As you know, the prepositions "beside" and "next to" are more or less synonymous. However, there are some nuances between them. Long story short, "beside" is more formal than "next to" Also, "beside" means there is no space between the two things. So they stick together. While, "next to" means there is nothing else between the two objects. However, they could be separated by some space. On the other hand "by" means "near", but a lit closer than "near". Irrespective of the fact that "beside" is more formal and "next to" is a bit more casual, I was wondering whether I have been wrong in defining the following pairs as correct or incorrect:

1.a. Come and sit beside me. (Correct)
1.b. Come and sit next to me.(Incorrect --- doesn't sound idiomatic to me)
1.c. Come and sit by me.(Incorrect --- the same as 'b')

2.a. I live beside the sea.(Correct)
2.b. I live next to the sea.(Incorrect)
2.b. I live by the sea.(Correct --- the most natural to me. However it depends on the space between the sea and the house.)

3.a. I parked my car beside the post office.(Incorrect)
3.b. I parked my car next to the post office.(Correct)
3.c. I parked my car by the post office.(Correct)

4.a. There is a shop beside my house.(Correct)
4.b. There is a shop next to my house.(Correct)
4.c. There is a shop by my house.(Correct)

Please help me to be able to distinguish between these two prepositions.

PS. I have considered the similar thread. Unfortunately, I didn't find it that helpful, though.

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