1. I ride my bike to school.

2. I go to school by bike.
3. I go to school by my bike.
[Does #3 mean #1? Is #3 grammatical?]

All three are fine, yes.

Yes, sentence #3 "I go to school by my bike" means the same as sentence #1 "I ride my bike to school." However, sentence #3 is not grammatically correct. In English, we use the preposition "on" instead of "by" when indicating the means of transportation. So, it should be "I go to school on my bike."

Yes, #3 means the same thing as #1 and #2. However, #3 is less commonly used and may sound awkward or non-standard in English. The correct phrasing would be either "I ride my bike to school" or "I go to school by bike."