basically correct,at least i can understand the sentences totally. i have some tips though , if you dont mind
1: get up...may i excuse me, in real life, it always means the you know....some organ which only the males' have...is up...therefore, to avoid such awkward, we always us "wake up " instead.
2:minor errors here.
let me rewrite ...
a:Everyday when i wake up, my dogs stand in front of the door of my bedroom and wait for me. They make me happy everyday. I think that I cannot live without them, because they are very important in my life. If I dont have them , I would be sad.
tips: would is always used when you are describing something hypothetical.
b:I bought my second dog to he is taking of my other dog(i was totally lost....couldnt get your point sorry). Now they always play together. On the other hand(i can understand you were trying to practice"on the one hand, on the other hand ", however, here is not the correct place to use it..."Besides that," is a better option )I bought two birds, because I like birds as well.
tips: the perfect tense only works when there is a consequence afterwards.
I prefer my birds to other birds, because they learn words and songs more quickly.
tips: would rather than
c: I think that my pets must be better because they are doing run free.(sorry ,your pets were sick and getting better now?)