1. I saw tom three days ago.

2. I saw tom three days before.
(Are both OK?)

3. I arrived there after three days.
4. I arrived there three days after.
5. I arrived there three days later.
(Which ones are grammatical?)

6. I will meet Tom after three days.
7. I will meet Tom in three days.
8. I will meet Tom three days later.
9. I will meet Tom three days after.
(Which ones are grammatical and commonly used? Thank you.)

1. I saw Tom three days ago.

2. I saw Tom three days before.
(Are both OK?)

3. I arrived there after three days.
4. I arrived there three days after.
5. I arrived there three days later.
(Which ones are grammatical?)

6. I will meet Tom after three days.
7. I will meet Tom in three days.
8. I will meet Tom three days later.
9. I will meet Tom three days after.
(Which ones are grammatical and commonly used? Thank you.)

1 is fine; 2 would be fine if you complete the thought -- before what?

5 is the best; 3 is OK; 4 (again) would be fine if you complete the thought -- after what?

Each could be OK, depending on what you mean and if you complete the thought (9).
~ 6 and 7 seem to be referring to the future: Three days from now, I will meet Tom.
~ 8 is OK depending on what the sentence before says, so that the question would be answered -- later than what?
~ 9 needs to be completed -- after what?

1. "I saw Tom three days ago" and 2. "I saw Tom three days before" are both grammatically correct, but they imply slightly different things. "Three days ago" refers to a past event happening three days in the past from the present moment, while "three days before" refers to a past event happening three days before another specific event mentioned in the context.

3. "I arrived there after three days" is grammatically correct, but it may sound a bit unnatural. A more common way to express this would be to say "I arrived there three days later" (5) or "I arrived there three days after" (4).

6. "I will meet Tom after three days" is grammatically correct, but less commonly used. A more common way to say this would be "I will meet Tom in three days" (7) or "I will meet Tom three days later" (8). "I will meet Tom three days after" (9) is also grammatically correct, but not as commonly used as the previous options.

In summary:
- For expressions that refer to events in the past, "X days ago" and "X days before" are both commonly used.
- "X days later" and "X days after" can be used to indicate an event that happens in the future.
- When talking about future events, it is more common to use "in X days" or "X days later" rather than "after X days."