Is it permissible to travel for Ziyarat e.g to Najaf and Kerbala during ramadhan for less then 10 days in each place? E.g. 1 week in Najaf and 1 week in Kerbala (from the UK). And if it is permissible, would we have to miss the fasts and repay later on or can we fast whilst over there?

1- Yes it is permissible
2- The person cannot fast while there, but he would make up those missed days after the month of Ramadhan