Deshou is a variation of "desu" while darou is a variation of "da". In this context, "deshou" sounds formal so I would recommend you to use deshou in conversations or when writing in desu/masu style. However, when adding "to (と) + verb", we always use "darou". e.g.) sou darou to omoimasu. chigau darou to iwaremashita. I often hear learners of Japanese saying "deshou to omoimasu", which is a typical mistake.

Yes. Deshou is formal though.