If you even study Japanese as your main subject, how come you don't write in at least Kana? It is absolutely necessary to at least know the Kana. These are the absolute basics. 

Anyways:

Nihongo wo benkyou shiteimasu.日本語を勉強しています/にほんごをべんきょうしています. Since you are studying right now and I assume you wanted to say that you are studying it right now, it needs to be "shite-imasu". Just "shimasu" could mean a lot of things such as you will study it in the future or anything. Well, in your context anybody would understand what you are saying so this is just a grammatical thing. And even better would be "Nihongo NO benkyou WO shiteimasu".

J-poppu no ongaku to nihon ryouri　ha/ga daisuki desu.ジェーポップの音楽と日本料理は/が大好きです.ジェーポップのおんがくとにほんりょうりがだいすきです. Something "wo" suki desu is a combination I never heard and am sure of it not being correct. Something "ha" or more stronger "ga" suki desu is the correct form of using to like - suki. If you want to point out how much you like something it is totally enough saying "dai"-suki. You know, Japanese are usually shy anyway so they wouldn't even take so much use of "daisuki". But to be more kind of individual, you can certainly say "sugoi suki desu" and such. Or just "hontou ni" suki desu, meaning "I really REALLY like...".

Watashi wa neko wo katteimasu.私は猫を飼っています.わたしはねこをかっています. For anymals, you use "kau", which is conjugated the same as the "kau" that means "to buy". You can differentiate them through Kanji. kau - having a pet is "飼う" whereas kau as in buying is "買う".