1. Vivien and Fiona visit their friends on every Friday.

2. Vivien and Fiona visit their friends every Friday.

3. Vivien and Fiona visit their friends on Fridays.

4. Vivien and Fiona visit their friends on Friday.

(Are all grammatical? Is Sentence 1 right? Thank you for your help.)

2, 3, and 4 are fine. 1 is not quite right -- no need for the word "on" or the word "every." One of them needs to be removed.

All four sentences are grammatically correct, but there are slight differences in meaning and structure.

1. "Vivien and Fiona visit their friends on every Friday." This sentence suggests that Vivien and Fiona visit their friends on every single Friday, without exception. The use of "every" emphasizes routine and regularity.

2. "Vivien and Fiona visit their friends every Friday." This sentence is similar to the first one, but it does not include the word "on." It still conveys the idea that Vivien and Fiona visit their friends every Friday without exception, but it is slightly more concise.

3. "Vivien and Fiona visit their friends on Fridays." This sentence indicates that Vivien and Fiona visit their friends on any Friday, without specifying that it happens every week. There could be some weeks when they do not visit their friends.

4. "Vivien and Fiona visit their friends on Friday." This sentence suggests that Vivien and Fiona visit their friends on a specific Friday, without indicating whether it happens every week or just occasionally.

In conclusion, all four sentences are grammatically correct, but they convey slightly different meanings and levels of regularity. The choice among these sentences would depend on the specific context and the intended message.