How to politely request to magazine editor for the following issue?
Changing a figure and / or title of a manuscript during proofreading isn't a problem. At most, the production team might wonder if you're changing something that shouldn't be changed (e.g. if the author amends the paper to conform to reviewer comments, and then changes it back during proofreading, we have a problem). However you've given a sensible reason to make the changes, so in all likelihood the production team will just make the changes and move on to the next paper.

As for the letter itself, it's a bit deferential, but journal production administrators see a lot of such letters and won't be fazed. The only thing I'd suggest is that, since you say minor editorial changes are necessary, to also include these in the email, e.g. "on page 2 line 5, change "delete the word 'personal'". This speeds things up: the JPA can make all the changes and the typesetter can implement them at once. Without these changes the JPA would have to write back asking what other changes you want to make before he can pass the manuscript to the typesetter.