"If he knows" sounds like he may or may not already know. While "If he finds out" sounds like he doesn't know already but may know in the future.

Test Notebook Entry

This is a test. Please ignore. Thank you! 这是一个测试。请忽略。谢谢！

<pre class="tw-data-text tw-ta tw-text-medium" data-placeholder="Translation" id="tw-target-text" data-fulltext="" dir="ltr" style="unicode-bidi: isolate; background-color: rgb(255, 255, 255); border-width: initial; border-style: none; border-color: initial; padding: 0px 0.14em 0px 0px; position: relative; margin-bottom: 0px; resize: none; font-family: inherit; overflow: hidden; width: 275px; white-space: pre-wrap; color: rgb(33, 33, 33); height: 72px; font-size: 25px !important; line-height: 36px !important;">這是一個測試。請忽略。謝謝！這是一個測試。請忽略。謝謝！ 這是一個測試。請忽略。謝謝！</pre>

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Your dog seems so cute; he's certainly a big part of your family!

Mainly, the changes below are about verb tenses. You should, first of all, keep your tenses consistent. You start the writing with "is" -- so keep the rest of your verb tenses consistent to this. Also, try to avoid the passive voice. Since you are describing behavior that your dog normally does on a daily basis, keeping the active present tense makes more sense.

My Dog

My dog is good at eavesdropping. He tilts his head as he listens in on a conversation. Suddenly, he dashes towards where we're talking. He catches onto words like "meat," "go outside," and "eat." He's good at peeking, too. When I'm in the bathroom or in the shower, I catch him peeking through the slit in the slightly opened door.

In the afternoon, he takes a nap. His coat looks fluffy and soft. I creep toward him, but he knows and already starts to groan as if saying "keep your hands to yourself. Do not touch me." I just backtrack. 

At night, he makes the rounds of visiting different rooms. He goes to bed in my parents' room at first, and then moves to my brother's room, and then to my room, the final destination. When somebody leaves home for days and comes back, he goes to bed in that person's room and wakes up in the morning in the same room.

measured

"She is to solve..." doesn't sound natural. Unless, you mean: "She's to solve..." a contraction for "She has to solve..." which is correct but may sound like "she is to solve". In that case, "she is going to solve..." and "she has to solve..." would mean two slightly different things: 1. She is going to solve... : She is in the process of solving (or) she will solve it in the future... 2. She has to solve... (She's to solve...) : She has been given a problem that she must solve.

I can imagine that both A and C would be acceptable usage in American English. It means that my house and his house are located in the same hill. However, my house is at a higher altitude than his. So, maybe my house is on top of the hill, and his is half-way up the hill :)