It takes total of 10 days to go to Kingdom of Mismede capital city from Alephis Capital City using carriage, which will takes 6 days to arrive at Great River Gau and another 4 days to arrive at the Mismede's capital city.
「Gate」 could not be used inside/onto magic barrier.
The Royal Castle has been protected using magic barrier to protect from any 「Gate」 like null magic except inside Yumina's bedroom.