If a person is unable to combine the 'aqiqah and the vow, which one takes precedence, and is it permissible to delay the vow in order to perform the 'aqiqah?

If your friend did not specify a time for his vow, then he may offer the aqīqah at its appointed time, which is the seventh day for the newborn. This is because fulfilling a vow is not immediately obligatory unless a specific time has been set for it; rather, it is permissible to fulfill it at a later time. It is also permissible for the vow and the aqīqah to share one camel or one cow.