Does Thomas S Monson answer questions on Twitter?

I want to ask him if we should create a video game &/or an anime of the Book of Mormon. I think this could really benefit members in Japan & all over the world. Using member's in Japan culture could help the church grow their. I don't know if this would be ok to do. I just want to help.

As near as I can tell, President Monson's official Twitter account has never responded publicly to any tweet. I don't know if those who monitor his account would respond to a direct message; I rather doubt it, but you're welcome to try.

But as for your question about creating a video game or anime of the Book of Mormon, I see no reason why you couldn't simply choose to do it. The scriptures counsel us to "be anxiously engaged in a good cause, and do many things of [our] own free will" (D&C 58:27). In the 2015 LDSTech App and Game Contest, dozens of developers created all sorts of apps, many of which had a Book of Mormon theme. If you have a good idea, you could certainly choose to create an app or video on your own (respecting the copyrights and other intellectual property rights of the Church, of course).

And if you're not sure whether you need permission from the owner of the IP, you should contact the legal department (which is where Pres. Monson or his staff would send you): https://www.lds.org/legal/terms?lang=eng

Thanks for responding to my question.