Class X CTs are normally used in conjunction with differential or high impedance protections. Is it okay if the same CT is used for other protections e.g. overcurrent, unbalanced load, impedance etc.?
Yes it is ok technically. Only issues are obviously the cost of these CTs and also you need to check the dimensions of these CTs if you have enough space to install them for your application.
As the class X CTs have very high saturation current (high accuracy limit factor or ALF) make sure that the relay rating is adequate. Otherwise you have a risk of damaging the relay. Normally the relay can handle 30 x In for few seconds. So generally it should be fine. But rarely, there could be an issue due to the high fault current and the low CT ratio.