It depends.
Not exactly. Although they are very similar, computer science and computer engineering are slightly different. Computer science tends to focus on software and programming. Computer engineering focuses more on hardware, like computer chips and hard drives. There is a bit of overlap though in that computer engineers may do some programming and computer science specialists may occasionally deal with hardware.
programming. Hard design software. Working with network. and any other work-related to information technology.
I suppose that is possible to have success with minimal efforts in programming (of course, don't be completely stranger).
hard drive on the computer, it does the programming
The hard drive with the necessary programming is the core of the computer.
No, you probably won't fail computer science. Probably. Mathematics involves logic and problem solving - which is a major part of computer science. Although programming is also a big part of computer science, there are quite a lot of branches to do with computers, and you don't necessarily have to work with programming. I'm good at maths and not so good at programming but I still did pretty well (better than all the hard-core programmers) in the computer science / programming class. If that's any consolation.
The Hard Drive
All forms of engineering are "Hard". That is, they take years of study of very technical topics. If it is what you are interested in, the difficulty will not bother you. If you are not particularly interested it will be VERY HARD.
It is really hard to explain in a few words; I suggest you register for an introductory course in computer programming, to get an idea. For example, there is a good course at udacity (using the Python programming language).
No it is not
See pharmacology, engineering, chemistry, electronics, computation / computer programming, etc. The uses are so plentiful you would have a hard time detailing them all in even a 50 page paper.
Well for me Computer Engineering seems to be the toughest of all engineering branches, because it incorporates lot of other fields.For example as a computer Engineer, you have to have a good understanding of mathematics, circuits, and several others. One thing with ECE is that u have to treat electronics engineering, electrical engineering, communications engineering(for network design), computer science and Logic(for simulation and robotic processes). however with hard work everything seems easy!