ze mazkír li otó.
Is the order of the לי and the אותו important here? I put זה מזכיר לי אותו .
It is. Your sentence is great, and it's the suggested translation, so I'm not sure what exactly you mean, but the לי has to be adjacent to מזכיר.
So it cannot be "zeh mazkir li alive"?
"זה מזכיר לי עליו?" Is this an acceptable alternative?
No. מזכיר comes with את (or without a preposition if the object is not definite).
Instead of זה I used הוא. Is that incorrect? Would הוא only be understood as referring to a person?
Should be OK. הוא can be an object.
"something else/זה מזכיר לי "על/ב אותו ?
Why can't אותו precede לי?
Vis-à-vis a second pronoun, -ל generally has precedence.
Why is the pronunciation mazGir rather than mazKir ?
Hmmm. I'll check with a native Hebrew speaker, but using עליו rather than אותו does sound better. The "of him" would equate to "about him" so it will depend on whether להזכיר needs a direct object.
You don't need to check with anybody else. radagastthebrown is a Hebrew native speaker and he already wrote it requires a direct object.