Student or Learner
which phrase is a correct english expression:
"give me a space" vs. "give me space"
"give me a breathing room" vs. "give me beathing room"
Welcome to Using English.
Please remember that capital letters are an important part of correct English.
In both sentences, omit the "a." The one with "breathing room" would be much improved with "some" - give me some breathing room. The one with "space" would be slightly improved with it.
Room and space both have uncountable meanings, like you have here, and countable meanings.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.