Does the vow take effect with the plural form, "vowing and dedicating our lives to my home/my country," and is this phrasing considered binding or a figure of speech? And does the explicit vow apply only in legal rulings, or is it a matter between the servant and his Lord in religious practice, based on his intention?

A vow (nadhr) is a commitment to an act of worship that is not obligatory. The stated phrase, "We vow and dedicate our lives to my home or my country," does not constitute a valid vow, as it does not involve any commitment to Allah Almighty. Scholars do not differentiate between a fatwa (religious ruling) and a diyanah (religious practice) concerning vows; rather, they differentiate in some matters related to divorce. It is advised to turn away from obsessive thoughts and disregard them.