Mon animal préféreé

"préféré" is good, just mentioning the alternative "favori" in case you are looking for vocabulary ;)

Mon animal préféreé est le chat.

We need an article here, I think the idea is that we are referring to a concept : "le chat" as cats, the idea of cat, the concept of cat. Note that you would also need an article if you want to designate a specific cat "j'aime le chat des voisins", "j'aime ce chat, là bas, le blanc et noir qui dort sous le buisson.".

J’adore les chats parce- que 'ils sont adorables et non agressifpaisibles.

"parce que il" => "parce qu'ils"
"non agressif" : it is correct but weird in the context. Fits, we would rather say "ils ne sont pas agressifs", and second most of the time we would use a negative construct only when we want to emphasise that this is the opposite of what is expected : "Mon chat n'est pas agressif." not only means that your cat doesn't scratch nor bite, but that you think that your interlocutor thinks cat usually do.
So we would go for antonyms of "agressif" : "paisible", "tranquilles", "calme"... pick one

Btw... I met cats that were pretty much agressive. I can tell you that it does not matter you weight 15 times more when you see the dilated pupils of this berserk driven creature equipped with lethal weapons... And I tell you this as a cat lover :)

J’ai quatre chats au mà la maison, mais ils mangent trop !

- "à la maison" would be the correct way, and "chez moi" is a descent alternative.
- "mais" is not really a good pick here. It is, I think, a rather good equivalent for "but" in the sense that it materialises an opposition or an exception to a rule. Either a rule that is known or one that you introduced in the present text.
"J'ai quatre frères mais pas de soeur." (here "pas de soeur" is an opposition to "j'ai quatre frères")
"J'ai une poule mais elle ne pond pas d'oeufs" (here we have the implicit rule that hens should lay eggs)

In your sentence there is no opposition in the sentence, nor in the next, not even with an implicit know rule. Therefore I'd rather go with :
"J'ai quatre chats à la maison et ils mangent trop !"
Where "et" simply allows for adding another information to the subject introduced at the beginning of the sentence. Alternatively you could write.
"J'ai quatre chats à la maison. Ils mangent trop !" That would be similar in meaning, but the short sentences gives a feel of "well... I know... I shouldn't indulge them so much food...".

Mon animal préféreé

Mon animal préféreé est le chat.

J’adore les chats parce- que 'ils sont adorables et inon agresffensif.

"inoffensifs" sonne plus logique dans cette situation. N'oublie pas de faire la liaison entre "que" et "ils" car "ils" commence par une voyelle

J’ai quatre chats au ma maisonchez moi, mais ils mangent trop !

"chez moi" paraît plus fluide. "dans ma maison" ou "à ma maison" aurait été possible également