Student or Learner
1) Usually this shop is the last one to close.
2) This shop is usually the last to close in the mall.
(Not a teacher)
I guess we could nit-pick and say the first should include a comma, i.e. "Usually, this shop is the last one to close."
Grammatically, they are both fine. The only difference is you are moving the position of the adverb. As for the removal of "one" in the second, I'm not sure if it is grammatically correct or if it is elliptical. However, the sentence isn't any more ambiguous, so it seems fine to remove it.