If fertility rates remain below replacement levels, then eventually we will go extinct. How far below replacement determines how quickly this will happen.
The low fertility rate is not very uniform across cultures. Some pockets of society have high fertility rates which would keep things going. Also, fertility rate cultural norms can easily reverse a few generations down the line.
Yes, and at current rates it would take many, many generations for extinction to occur. Do the math with whatever birth rate you want to use. It’s not like birth rate is likely to stay constant over such a long period, either.