Well,you can learn to write a "hello-world" program in 10 minutes.But really learning the language can take up to years.It depends on the person,how fast you can learn,and of course how much you study it.
I don't know if other people would agree, but I don't think someone new to programming (as you've said you are) can sit down and study one language and say 'I understand about x% of C++' after n months. You should be more concerned with understanding programming concepts rather than syntax. To answer your question, after a month of studying the basics of C++ you might know about its data structures, class construction, inheritance, exception handling, etc. Whether you can write anything useful at that point is up to you.
It depends. For me, at that point, I could write minor apps, but the code structure was pretty poor. The code was all jumbled up and inefficient. At some point, you should work on making your code more coherent and able to flow smoothly. Pick up a book or two, they will teach you how to make your code better. I recommend Big C++, and Learn C++ in 21 Days. DON'T pick up Learn C++ in 24 HOURS. just don't. Most important of all, HAVE FUN!