In addition to above, you can say, "I'm a new father.", etc.

Newly married and newly single are correct, however it is more common to say "recently married" and "recently single" ("recently divorced") is more common, but people will understand what you mean if you say "recently single". Because "Mother" and "Father" are both nouns, you would need to place the article "a" before them as well as include a verb. "I have recently become a Father" "I have recently become a Mother" Hope this helped :)