Yes, Germans can apply for an Oman visa. 

If within 24 hours and your visa has not yet been submitted to the embassy or paid yet at the immigration, then $70 will be deducted from the refund. After 24 hours, you will get 50% of your refund but only if it has not yet been submitted to the embassy. Once it is submitted, you will not be able to get a refund if you cancel your Oman visa. 

The recent immigration rules mention that German citizens need a visa to stay in Oman for more than 14 days. However, if the stay is going to be for less than 14 days, then a visa is not required. 

Children between the age of 2-15 traveling alone will be classified under "unaccompanied minors" and cannot travel alone.