I can answer the first part of your question better than the second part. I use computer science and coding, but I am not a computer scientist.
There is definitely math in computer science. In particular, you need to use a lot of the logic of math. For example, if you wanted a program to do something a certain number times, you would need to create a way to keep track of how many times it has already done it. You might put a sum in there and then tell the program that once the sum reaches a certain number, stop doing whatever it was doing.
As to what computer scientists do on a day to day basis, I can answer from having friends who do it. I believe that they write code most of the day. This is like tricky problem solving - you are trying to get a program to do a certain thing and you are trying to come up with the best, most efficient way to do that without using a lot of memory. So being a computer scientists involves a lot of solving puzzles. But a computer scientist might be better able to answer this part of the question.