Can I cast spells in the middle of another spell resolving?
No, Cloudshift is resolved as a single, atomic event.  There is no time in between the parts of its effect in which anyone has a window of opportunity to cast a spell.

From the Comprehensive rules:


  116.2e Resolving spells and abilities may instruct players to make choices or take actions, or may allow players to activate mana
  abilities. Even if a player is doing so, no player has priority while
  a spell or ability is resolving. See rule 608, "Resolving Spells and
  Abilities."