To view the Cross Universe terms of service, please refer to the official website at crossuniverse.jp/約束事.
Quick Summary
(This summary is just provided as a convenience and may not be 100% accurate. For definitive answers, check the official terms above.)
The cards can be used non-commercially for most things, as long as you follow these rules:
Do not edit or modify the cards without getting permission first.
Do not use the game for malicious things.
Do not mislead people into thinking that something you made based on Cross Universe is official.
Include attribution and a link to crossuniverse.jp in things you make, if possible.
For commercial use, the restrictions are more detailed, so please check the official terms for those.