The correct grammatical forms are: (mój) kochany (m.) (moja) kochana (f.) (moje) kochane (n.) (rarely used in 2. person, rather in 3. person like in "moje (u)kochane dziecko/kocię/miasto" = "my beloved child/kitten/city")
(moje) kochanie is another thing, b/c "kochanie" is verbal noun (gerund) and not adjective used as noun (like kochana/kochany).
You can say "kochanie" if: 1. you are referring to your beloved one (to man or woman) = "my love", in most cases without "moje", but not always ("Kochanie ty moje!!!" = "Oh, my love!!!") Can be used in almost every sentence ("Podaj mi kochanie pilota! Przynieś mi kochanie piwo!" "Give me the remote, darling! Bring me a beer, my love!") You can also use some diminutive words, especially animals (genus depending on its grammar gender). To a woman: żabciu/myszko/rybko (froggy/mice/fishy) To a man: misiu = teddy/small bear 2. you are talking sweet way to a kid (even if it's not your kid) = "sweetheart"/"sunny" ("Jak się kochanie nazywasz?" "What's your name, sweetheart?") etc.
You can say "kochana" (to a woman) / "kochany" (to a man) if: 1. you are talking about your beloved one to another ppl: to friends or family members ("moja kochana się obraziła" = "my wife/gf took offence") 2. you are trying to force kindly someone to do something for you or you disagree, in most cases not nice b/c it's only formally polite ("Nic z tego, kochana!" = "No way, darling!"). Sometimes you can use "kochana" instead of "kochanie", but be sure the sentence will not sound impolite ("Kochana, idziemy do kina dzisiaj wieczorem?" / "Are we going to the cinema/movies this night, darling?") 3. sometimes between women, like saleswoman to the client, very informal and only in small shops of both women are 15-40 y.o. ("coś jeszcze kochana?" = "Anything else, darling?"); you can sometimes hear that also spoken to a men, especially if you are 20-25 y.o. and saleswoman is a bit older :-) 4. you are very thankful, so you can say informally "Jesteś kochana/kochany! Nie wiem, jak się odwdzięczę!" = "You are loved! I do not know how to return the favor!" and give a big big hug; it's informal and used only toward friends and family members, especially if both are girls/women ;-) 5. about something most favourite ("to moja ukochana/ulubiona sukienka" = "that's my favourite dress"/"that's the dress I love most") etc.
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