If you cancel your application after 24 hours, you will get only 50% of your refund only if it has not yet been submitted to the embassy. In case of cancellation within 24 hours, you are eligible for a refund on two conditions i.e. your application has not yet been submitted to the embassy and your $70 will be deducted from your refund. If it has already been submitted to the embassy, then no, you will not be able to receive a refund if you cancel your Oman visa application. 

Yes, you can apply for your Oman tourist visa from Hong Kong by applying for it online through Oman IE Visa. 

You will get your Oman tourist visa sent to your email. You can also download your visa from the website. 

Yes, you can. However, your pet might require a permit while traveling to Oman.