One of the classes I'm taking in college is where we are doing a ton of programming in C. We are supposed to use 'C' style naming conventions in the assignments or get docked marks (eg a variable is named like int line_counter, a function clear_array() ) I find this convention really really annoying esp coming after a year of Java where such things are named more conviniently like lineCounter or clearArray(). Underscores are annoying, a hassle to type and increase the amount of syntax errors. Why should this convention be followed? Is there some logic to it or some point behind it? Or is it just another trick to make 'C' even harder to write code in?
Style naming conventions are a matter of tradition, local agreement and uniformity. You have to get used to a different style because there's no guarantee, once out in the job market, that you will use the code convention you like. In this sense, the point is that you have to learn that the Java style is not the only style you will ever deal with.
On regard if it's a good decision or not, it's hard to decide. I am annoyed by styling violations as you are, even if I have tens of year of experience in programming, but you cannot really pretend to reform an old code to new conventions. It takes a lot of non-productive time and screws everything for the other programmers.
You can mitigate the problem of slow-to-type-underscore using tab-completion in your editor (e.g. vim). Writing a method will just become typing a few letters and pressing tab. It's unlikely you will hit an underscore in the first letters.
Getting used to a specific style convention is just a question of the number of lines of code you have written. In this case, that that you find annoying in C because you were used to Java, is also a convention in Python: Contrarily to you (I program mostly in Python), I like better the underscored variable names (although I understand the java ones are also very clear to read)
On the other hand, and as a curiosity, you probably know that the difficulty to write a given character depends on the local distribution of your keyboard. Many of the symbols used in C are a hell to write with, for example, a Spanish keyboard.
What I think it is a really bad idea, is not to use the standard conventions for the language and develop a custom convention. This is really bad for others and also for you because all the documentation, code etc you have to study or interact with will be written in the standard style for the language
There is no such thing as "C-style naming conventions"; you will find quite a number of different styles both in C code and in C++ code. That said, you will just have to suck it up and go with the convention required by your professor. The purpose of style conventions, in general, is to reduce errors and to make it easy to infer information about a symbol without needing to look up its declaration. That said, there are many differences about which style or styles are best. Having a consistent style, though, is important for the understanding of the code base as a whole, and it is probably easier for your professor to grade and understand the homework if it is all written using the same, consistent style.
Pretty much any company you work for will require you to adhere to the company's coding convention, so it is not unreasonable for your professor to have similar requirements. Although it took some getting used to Google's C++ coding conventions when I first started, it is undoubtedly a boon to the code's readability to be in a consistent style. Nothing is more unintelligible than a mix of different styles.
I disagree with your teacher's decision to dock points for capitalization, but you're going to have to follow his or her instructions.
Grades are intended to reflect understanding of the material. I personally found it sufficient when teaching introductory C courses to grade on understanding. Beginners have enough difficulty mastering language constructs. It is unnecessary and cruel to dock points for trivialities.
The merits of your teacher's particular style, or of following a corporate style, are separate questions.