the first one is people with royal blood but it can be through relatives... the second one is the imperial family itself
I remember that the Chinese had an interesting practice where if they wanted better diplomatic relations with another country, they would "marry a princess" to the other country. However, if they did not want to sacrifice their own offspring, what they would do is that they would "adopt" a "princess" from somewhere, then marry her off instead. I guess this would be the key difference between "Royalty" (albeit a sort of fake one) and "The Imperial Family".
Which language? They seem to have slight differences in definition in Japanese and Chinese dictionaries, which makes sense.
Already did. One is the Imperial Family (actual) while the other is a huge court of adopted sons and daughters and Godsons and Goddaughters (Godson and Goddaughters were a thing in China) and adopted "Kings" to administer the border regions. You can sometimes see this in Chinese Xianxia where a "King" is a relative of the Emperor sent to administer a region, who may not even be blood related. Come to think of it, even Rome did that. Augustus Caesar was the adopted son of Julius Caesar.
Depends how far down you go in history. Early on, the adopted children were taken in for the role of taking over. Further down, military generals started letting the power go to their head and would make attempts to rule.
One is oushitsu, the other is ouke. 王 Ou is from the Japanese word for king 室 Shitsu means room, house or exclusive space 家 Ke can also be pronounced as Ka, which means family, such as 家庭 (katei) household and 家族 (kazoku) family. So 王室 (oushitsu) means the royal household. 王家 (ouke) means the royal family itself. Technically, royal household would include the maids, direct servants, the direct advisor or the brother or sister of the current king who is still not independent. Royal family would only refer to the immediate royal family. However, since the stories often gives different interpretation of what is 'royal household' or 'royal family', this could go either way.