As the shliach tsibur, should I hit my chest for s’lach lannu during the repetition?
Yes you should, as this is the minhag.
As a side point, when the Shliach tzibbur repeats the Shemona Esrei, it is his main davening. It is also a much stronger tefilla then the silent one. I once heard from a big Rov, that it is brought in one of the seforim that when we daven the silent Shemona Esrei it has to be said quietly, in part so that the malachim shouldn’t be able to block it, however chazaras hashatz is so powerful that even though it is said out loud, the malachim can’t block it! Additionally, the Vilna Gaon used to say, regarding the gemora Brachos 32a, “If a person sees that he davened and wasn’t answered, he should daven again”, this means chazoras hashatz. Meaning that by davening chazoras hashatz it can help the person that his tefillos should be answered.
Daas Noteh 1- Question 281.