Other users have already posted great corrections, so I will fill in the ones without any explanations.

Writing Tip

When writing English essays, we are taught to finish a thought with a period. In Chinese writing, we tend to “run on” until we feel like we have finished our “one” thought. For instance, it makes sense to group my name & my age together since both thoughts are describing me. Think like a Chinese when you are writing :D You have to ignore English writing rules. In conversation, you will be completely fine though.

我今年十九岁 vs 我十九岁

今年 means this year, it clarifies any possible misunderstandings.

我十九岁 is just fine. Suitable for answering questions such as “你几岁？”

还 as in 还有一只猫

还 in here means also

I have two brothers, one sister, and also a cat.

Quoting Raven’s answer, “我有两个弟弟和一个妹妹，我还有一只猫。” ← this reflects the writing tip that I was mentioning earlier.

口 & 个 for counting family members

They are interchangeable. You can use 个 or 口 for describing family members - 我家有六个（口）人。 口 might be easier for some people to remember because 口 means mouth as you have mentioned, so think of it as “every one person = one additional mouth to feed” ;D