The chance of the water heater being damaged during a night time dip below freezing is slim. It takes an extended period below freezing to freeze a 6 gallon tank to the point of expansion and rupture. Multiple days below freezing with the heater not operating then you have a problem.
The small diameter plumbing pipes, now that's a different story. They can freeze overnight at just below 32 degrees no problem. The pipes are likely PEX so they should be ok but the fittings will crack or push apart from the pipe connections. Check around elbows first, they always seem to be the first to let go.
Fixing any plumbing leak with eternabond on the exterior of the tank or pipe is no real solution. The pressure in the plumbing system works against that sort of patch and failure is the likely outcome. A short term fix at best. I am sure someone has had success with external tape patching but it would be the exception.
If you find something broken or split replace the part, everything you need is on the shelves at your local Home Depot and the parts are cheap. In the case of the tank it can be welded by a professional with the right equipment. An Atwood replacement tank with no attachments, just a bare bones tank, is around $200.00
Is there any other source of water in the area, a fridge overflow, a low point drain left slightly open, water dripping from the roof, a drain pipe under the shower pan? Investigate before spending money, I learned that lesson the hard (expensive) way.
