How did Betty know that there had been at least one power outage? Well, if she never defrosted her freezer, she'd notice that all the ice had fallen off the top and sides and refrozen on the bottom. But even with a frostless freezer, she could simply have placed an ice cube on the bottom of the freezer. If the power had gone off for a significant time, the ice cube would have melted, or (since refrigerators have a fair amount of insulation), would have partially melted.
In order to know whether there were two power outages, we're going to have to assume that each power outage lasts long enough to warm up the contents of the freezer to room temperature (and that the room itself is above freezing!).
So let's suppose Cathy fills a glass with water, then pours that water into an ice cube tray and freezes it, then piles those ice cubes back into the glass, and stores the glass in the freezer.
If there's no power outage, then the glass will still contain cubes of ice.
If there's one power outage, then...the glass will contain a solid block of ice. The block of ice will actually protrude out of the glass, since water expands as it freezes. However, the water in the glass freezes from the outside in, so the surface freezes quickly, and THEN the shape begins to bulge upward, so the unfrozen interior water never has a chance to escape from the glass.
If there are two power outages, then the solid block will melt from the outside in. The ice on the rounded top bulge of the block of ice will melt and run down the sides of the glass. When Cathy looks in her freezer, she will see that the glass contains a solid block of ice that does NOT protrude, and about 10% of the water will have run out of the glass and frozen in a puddle around the base.
You might expect that the glass would break when the water freezes, but glass is strong enough, and partially formed ice elastic enough, so that the mass of ice deforms into a rounded shape that protrudes out the top of the glass. But if the glass is very tall, or the opening on the top very small, the pressure of the ice formation will be strong enough to shatter the glass.
If the glass is actually sealed, (think of a bottle of Coke), then the formation of ice will actually be retarded, because each ice crystal that forms will increase the internal pressure and this in turn slightly lowers the freezing point. The water will stay liquid at temperatures several degress below its usual freezing point. If you suddenly open such a bottle of Coke, the high internal pressure will force the liquid liquid to gush out, the carbonation bubbles will pop out of the liquid (even inside the bottle), and the depressurized liquid will freeze almost instantly within the bottle.
This raises another question. If you had a container of water, and you just kept lowering the temperature, what would happen? Would some ice crystals form? Would the whole thing freeze in place, without ice? Would it stay liquid forever?