If you don't find programming hard, then you are already in the minority as far as most computer science students go. There is no such thing as "computer handicapped", everything can be learned by anyone willing to invest the time.
1) Should I even be trying to pursue a career related to computer science when I'm pretty much computer handicapped? So far, this has seemed like a pretty easy class and programming isn't hard for me (and it isn't just because the teacher is easy, I have one of the few A's in the class). In order to pursue something in computer science, however, is my knowledge on programming alone going to help?
Northern california is probably the best place in the entire world to find a computer science internship. You are only a junior in high school though, so don't worry about this yet. Just work on projects that seem fun to you, and you will learn plenty. Once you have finished a year or two in college, then you can start thinking about internships.
2) What types of programs/internships/camps/classes relating to computer science could you suggest me to take (preferably over the summer)? I live in CA, so preferably somewhere in Nor Cal, but I'm open to any residential programs elsewhere in the U.S.
Concentrate on getting your GPA as high as possible, and do good on the SATs. These are the two major things which colleges look at. It also helps to have some extra curricular activities like club participation and sports.
3) I've also researched the major and have seen that computer science is very popular and hard to get into. Are there any classes I should be taking/take to help boost my college applications (I feel like just taking two computer science classes isn't enough). I know how internships at hospitals would look good if you want to major in the medical field, but I was wondering if there is anything similar for computer science related majors?
This depends on the job and the person. People who love what they do are more willing to stay up late working on projects. Some jobs expect 70+ hour weeks from their employees, but others (like mine) only expect the standard 40.
My dad is some type of engineer dealing with hardware. He seems to stay up very late (like around 1-2AM) doing work. Is this typical of hardware/software/computer related jobs? Is this just how all work in all types of fields are?
This is not true. It is actually a very good time to be looking for a job as a software engineer. I can't say it will be the same in 6 years when you graduate college though. This is not something you should be taking into consideration, just choose a major doing something you like, that should be your priority.
And it seems like computer-related jobs (software, engineering, etc) are becoming scarce. It seems like a lot of people are getting layed off. Do only the people who excel in computer science get the good jobs?