Is the product of 9 and twice m translated 9(2m) or 9(m+m)?

Answer 1

yes.

The two expressions are equivalent, since m+m = 2m

That said, I'd interpret
"product of 9 and twice m" as 9(2m)
and
"product of 9 and the sum of m and m" as 9(m+m)

That would leave open the possibility of something like

"product of 9 and the sum of m and k" as 9(m+k)