Additionally, I also wonder to which extent it is common that same person represents a country at both world championships and universiade.
Quoting from the site of FISU:
The Universiades and [World University] Championships are open to all student athletes that have not been out of university or an equivalent institution for more than a year, and that are aged between 17 and 28. Any association which is a member of FISU may enter a team or an individual competitor. Entries are accepted from any country eligible for the Olympic Games and from any national federation affiliated to the appropriate international federation.
In addition, the individual sports may have placed additional entry criteria on the participants in that sport (for example, a country can only delegate at most two athletes for most athletics events and both athletes must have achieved a certain minimum result in that event).
I can’t comment on how common it is for athletes to compete both in a Universiade and a World Championship/Olympic Games.