If it is any indicator, King Christian X only appears sparingly in Klaus Jonas' "The Life of Crown Prince William." It's been several years since I read it, but I checked the index to confirm and Christian only appears on three pages. The book does include the information, however, that then-Crown Prince Christian and Crown Princess Alexandrine were the first people that Wilhelm & Cecilie told about their engagement.
Was the future Christian X close to his b-i-l Crown Prince Wilhelm of Germany, namely before WW1? Did Wilhelm attend danish gatherings like the english and russian royals ?
I don't think they were close at all. Wilhelm's father, the Kaiser, had never been popular with the Danish royal family, so I assume Christian was a bit reluctant to welcome his son into the family circle. Crown Prince Wilhelm was a rare guest in Denmark, but here is a photo of him and Cecilie in Copenhagen some years before WW1 (the two boys are Frederik and Knud):
How were the relations between the 2 couples after WW1?
In 1918, Christian X cold-shouldered Wilhelm when the latter asked if he and Cecilie could possibly live in Denmark. The King told him that it would be politically too complicated to grant exile to the Crown Prince, but the Crown Princess would be welcome in Denmark. Wilhelm and Cecilie were rather offended by this answer to their request.
In the years between WW1 and WW2 the two brothers-in-law did, however, see each other on some occasions, for instance in Berlin in 1927, where these two photos were taken.
I think Alexandrine and Cecilie had a far better relationship than their husbands, although the exiled Kaiser at some point tried to stop the communication between them.
Prince Louis Ferdinand of Prussia, Grand Duke Friedrich Franz IV of Mecklenburg-Schwerin, Princess Friedrich Sigismund of Prussia, Crown Princess Cecilie of Prussia, Queen Alexandrine of Denmark, Prince Hubertus of Prussia, Grand Duchess Alexandra of Mecklenburg-Schwerin, Crown Prince Wilhelm of Prussia, Prince Wilhelm of Prussia, King Christian of Denmark and Prince Friedrich of Prussia.