Yes. It is also common to use Mrs. Miss. and Dr. AFTER the short form for example Cllr. Dr. James Walsh Cllr. Mrs. Rosie Orpin I have never seen Mr. used after the short form, so maybe it's assumed that all councillors are mister?
No, neither form (councillor, counselor) is an adjective. It is a noun (a person).
narrative
The short form of writing 4,352,697,109 is " 4.35 billion."
The short way of writing square root of x is sqrt(x)
While "prolly" is a short form of the word "probably" used in texting, it is considered to be unacceptable in any other form of writing.
cc is short for "carbon copy"
An abbreveation is a short way of writing things for example Young Readers Choice Awards is abbreveated as YRCA
Distinction does not have a short form. However, the short form of did not is didn't and the short form of are not is aren't.
The oldest form of writing was with pictures
The proper salutation for a doctor is doctor or professor depending on their title. In writing the short form can be used which will be Dr. or Prof.
The word 'particularly' should not be abbreviated. You can do so with what I use 'speed writing' such as 'prtcl/y' but that's just speed writing and not meant for short form in any other text.
Cuneiform writing was developed in ancient Mesopotamia, particularly in the region of Sumer, around 3400 BCE. It was one of the earliest writing systems in the world, consisting of wedge-shaped symbols impressed on clay tablets.