Hi! So, first of all 'and go on' is not correct. 'etc' is usually used informally when writing to a friend/family, whilst 'and so on' is used in a more formal way You can also use 'so on and so forth' too! 'and others' 'and stuff like that' (informal)

"Etc." is the most common in written English. "And so on" is a bit more informal. It is probably used more often in spoken English. "And go on" is never used.

"And go on" isn't correct. As for "etc." vs. "and so on", they can be used interchangeably, BUT: 1. "etc." is an abbreviation, so it should always be written with a period at the end, even in the middle of a sentence. In Spoken English we use the full term "et cetera". 2. These aren't typically used to refer to lists of people, especially not "etc." because it literally means "and other things" 3. "Etc." should only follow lists of 2 or more items, but "and so on" is sometimes used after only one example. You could say "My mother does the cleaning and so on."; meaning that she cleans, and also does other related household tasks (cooking, laundry, etc.). Besides these, you can also say "and so forth", or combine them into one term, "and so on, and so forth". The latter isn't that common; when I hear people use "and so on and so forth", it can imply that the list is too long, or that the items in list that aren't mentioned are unimportant. "And whatnot" is something you'll hear sometimes, although it sounds very colloquial/informal. "And the like" is similar, and more suitable for lists of people ("Pop stars, movie stars, models, and the like").

Hello! It seems to me that the phrase “and so on” sound more casual. You can also say “and so on and so forth”. That will sound more official. Etc is an abbreviation of a Latin expression “et cetera” , so it is also a little bit official but you can hear it quite often as well. I don’t think that “and go on” is used in the same context. Usually it means продолжать делать что-то)