Problem Starting Car Honda Fit 2015

I live in Montreal, Canada – a relatively cold place in winter. Yesterday, to my surprise, my car would not start. I was especially surprised since I bought a brand new, relatively expensive battery three months ago. I cannot remember what brand it is, but I ensured that it had a solid rating for winter use. Here are some facts of relevance:

– The car has been sitting for a week;

– The temperature the preceding night had been about -15 Celsius

– The preceding week had not been that cold – lows ranging from -16 C to -5 C. This is not really that cold for this part of the world and, historically, I have never had problems at these temperatures here, even with an older battery.

– When I turned the key, all I heard were a series of clicks. I did confirm that some of the interior electrics (e.g. dome light) were functioning, although at noticeably reduced levels.

Question 1: Does the ability of a battery to start the car depend only on its temperature at the time of attempted start? Or is also a function of the amount of time since the last start.

Question 2: It will get up to zero Celsius in a couple of days. Do you think there is a chance the car will start at this warmer temperature without a boost?

Question 3: Assuming the battery is the problem, does it not seem odd that a new battery would go so dead in such relatively warm conditions?

Thanks.