Question 1 - The water was cut off from the taps in my area at the time of Dawn (Fajr) prayer, my question is; Is it valid for someone to perform Tayammum (Dry Purification) in this case?

Anwser - Praise be to Allah and may Allah raise the rank of our Master Muhammad and protect his nation from that which he feared for them.

In the presence of suitable water, it is invalid to perform dry purification. In your case, you have the option to either access water from your neighbour or simply buy it.