There's just a few little errors. My Japanese isn't absolutely perfect, so anyone else can feel free to correct me if necessary! ^^
If you're trying to say "This is my Chandelier", (if by "Chandula", you do in fact mean chandelier) then it should be:
私のチャンデリアがあります。 Watashi No Chanderia Ga Arimasu.
If you like, the "Watashi No" isn't really needed and you can drop it. Though, it makes no difference if you don't. 
It absolutely changes the meaning of チャンデリアがあります from "I have a chandelier" to "there is a chandelier"
Furthermore, "This is my chandelier" is これは私のチャンデリアです。, just by "textbook" Japanese.
私の～ Watashi No.
"No" is the particle you use to say something is yours. Otherwise, the sentence as you wrote it reads as "I am the cat and the dog". Also, don't forget to change "Arimasu" to "Imasu" (your animals are living)...
and put a "Ga" inbetween "Ipiki" and "Imasu".
が goes before 一匹, not after.
You just need to get the correct particle and verb, and switch the sentence around a little. It should read:
私の寝室は家の後ろにあります。Watashi No Shinshitsu Wa
Uchi No Ushiro Ni Arimasu.
いえ
You just needed to change "Wa" to "No" and "Imasu" to "Arimasu", because your bedroom isn't a living thing.
I think I would say the following, instead:
奇麗
じゃない家です。 Kirei Janai Uchi Desu. My house is not pretty.
You do not mix じゃない with ます／です form
Though, if you want to keep it similar to yours:
奇麗な家がありません。Kirei Na Uchi Ga Arimasen.
I'm not 100% on this, but I THINK your version says "My clean house does not exist". It says "There are no pretty houses." Also, a careful writer of Japanese would not use kanji for きれい.
～います。 Imasu. Not Arimasu.
This says "The dog is noisy" or "I have a noisy dog" (if you're pointing at it or it's in the room). If you wanted to change it to "My dog is noisy" (assuming your dog isn't in the room), you might say:
私の犬は煩いです。Watashi No Inu Wa Urusai Desu.
Otherwise, what you wrote: you just need to add "Ga" between "Urusai" and "Imasu".
一つのテディー・ベアがあります。Hitotsu No Teddy Bear Ga Arimasu.
You say "Arimasu", because it is not living. You just needed to change sentence structure. It now says "I have one Teddy Bear".
～ありません。 It isn't living. And you forgot the "Ga" inbetween "Futatsu" and "Arimasu".
I hope I did alright, it was also a good practice for me!
Oh, and for future reference...
Imasu: To exist as a living thing, for example an animal or a human. Although plants are living things, they are Arimasu.
Arimasu: To exist as something that isn't living, for example, wood, a desk, toothpaste, a bottle...