Hi Zea, 
Good to hear from you. Sorry for the late reply to your letter because I've been busy with my final exam. Fortunately, I did it well. And I'll answer your question about the idea of having a pet right now! 
Don't worry if you are living in an apartment. Today, apartments are pretty open about keeping pets in our apartments, so you can keep any animal you want! It seems like you love dogs, right? Let's try to have a cute dog. I think you should buy an adorable, tiny, docile and intelligent dog like Corgi, Pomeranian, or Poodle because it might be easy for you to feed and take care of it. Don't buy naughty ones, it will annoy you and your neighbors. But if your apartment doesn't allow dogs or cats, there are still many animals such as fish or birds. They don't take up much space in the house and are very easy to keep. Do you know hamsters? They are rats. Despite being rats, they're really cute! I also want to have some hamsters one day. 
As for convincing your parents to let you have a pet, you can use my method below. Thanks to it, I was able to convince my parents and have Dudu like today. Show them all the pet's advantages like being cute and smart. Talk about the benefits of having a pet. You'll spend more time together, take the pet out together, and have something to bond over. Making promises is essential. You have to promise that you will take good care of it, don't let it bother everyone in your family,...
That's all for now. Write me if your parents let you have a pet or not.
Love
Hang