Is it permissible to perform I'tikaf on the odd nights of Ramadan due to an inability to perform full I'tikaf because of recent marriage and the wife remaining alone at home, knowing that the residence is next to the family?

The best is to perform I'tikaf (spiritual retreat) for the entire last ten days of Ramadan, following the example of the Prophet, peace and blessings be upon him. For those unable to do so, it is permissible to perform I'tikaf for some days or nights, such as observing I'tikaf for one night. There is no minimum limit for the duration of I'tikaf, and one should strive hard in worship during these nights.