1. We can save water when I brush my teeth.

2. We can save water when we brush our teeth.

3. We can save water when we were brushing our teeth.

================
Is #1 correct? Is it logical? Is #2 better and correct? Is #3 the best? Thank you for your help.

No, three is not best! It's wrong. "Save" is a present tense verb, "were" is past tense. Tenses should agree. The same is true, in a different way, for the first. We is plural, I is singular. Both pronouns should agree. Use either "I" or "we" in both the primary sentence and in the prepositional phrase.