Can watashino stand alone?? - Yes, it can. Which ones are right and wrong? - They are all correct. Watashi no kuruma da　私の車だ。 Watashi no desu　私のです。 Watashi no kuruma janai　私の車じゃない。 Watashi no ja arimasen　私のじゃありません。 "watashi no"「私の」 means "mine" in English. 「誰か財布を忘れていますよ。誰のですか？」（Dareka saifu wo wasurete imasuyo. Dareno desuka?/Someone has left a purse. Whose is this?) 「私のです」(Watashino desu./It's mine.)

Technically, it could stand alone as a response to the question: "Who's car is this?" You could say: "a, watashi no" or "a, watashi no desu." However, in my opinion, it sounds a bit awkward. の is a possessive particle. It is attached to a noun or pronoun connecting it to another noun. 私の車 (watashi no kuruma) = "my car" 私のノート (watashi no nooto) = "my notebook" etc. To me, without another noun being connected to の, it sounds incomplete, but conversationally, this is perfectly fine. All of the examples you have given are natural responses as well. By the way, the "conjugated" part of the sentence is the verb only. わたしの is not conjugated, as it is not the part of the sentence that changes. I hope this helps! Please let me know if you have any more questions. Best of luck in your studies!