Does it have a name? Some varieties are hardier than others. Also, where are you located?

Likely if it is a C japonica, it will. Most C. japonica can stand frost and light snow. unless it is a hybrid bred from the C. species from Vietnam or very south of China.

Yes, many people grow potted camellias in zones where they cannot be left outside during Winter. They stay inside during winter but come out during warmer months.

In general, plants with more access to the sun will flower more. So bring the camellia outside to a location that provides shade in the afternoon.

With some of my shade loving plants, I bring them outside "slowly". That means I choose a temporary location where they get just a few (1-2) hours of sun only. After 1-2 weeks, I move them out to their 'real' outside location until Winter, when I bring them indoords again.

Do not panic if the leaves show some sunscald at first. If the location provides morning sun only (3-4 hours) in the summer, this should be temporary.

Luis