I'm a California CC student as well, planning applying to Cal Tech for transfer. Here is my response to your situation from what I have learned:
Regarding research: there are plenty of opportunities for CC students all over the country/world... just dig and dig around for these opportunities via REU and SURF. Get in touch with your faculty at the community college or even a local university. They can have a lot of information for you in this matter, if not actual opportunities.
Regarding the caltech transfer exam:
Caltech has a list of subjects/topics that are on the test for both the physics and math portions. This is supposedly taken from their course curriculum. You can find all of their curricula for their classes under respective department web pages. I suggest self studying this material and looking at the homework problems, mid-terms, and final exams posted on the course pages. Most of them even have lecture notes.
As far as the test goes, from what I've heard, it is indeed mostly proof based. However, I heard from someone who took the test that there are some demanding computations involved. Since no calculators are allowed during the test, they assumed that the numbers would be small/manageable. They said that some of the numbers were incredibly large and difficult to deal with. Based on this, I've started doing all of my homework without a calculator (I use it to check answers), which is probably good practice considering that you won't be allowed one on tests if you do transfer to Cal Tech.
I also heard that the entrance exam is the most important factor regarding your transfer admission. If you don't pass it, they will not look at ANY of your application... it goes straight to the trash. As far as the rest of your application goes, I've heard conflicting information: some people say that you need tons of research experience, accomplishments, extracurricular activities, etc. in addition to a high exam score while others have stated that if you score well on the exam, they will be pretty interested in you as long as the rest of your application looks decent (as long as your essays are good and well written). I've heard the next biggest factor is actually your recommendations. If you can get physics professors, faculty, or those employed in the field (or whatever your desired major is) to recommend you whole-heartedly (ESPECIALLY if they teach at or graduated from Cal Tech themselves) you will be much more desirable.
The other thing that seems very important: take as many science classes from as diverse of a selection as you can. The prestigious schools seem to value taking several semesters each of Bio, Chem, Phys, and Math as possible. It also seems that the more foreign language you take, the better (for instance, I believe Princeton requires 4 semesters of foreign language).
If you do get accepted into Cal Tech, it seems most transfers do not transfer in at the Junior level. You will likely have to "retake" classes due to their demanding curriculum. So it may take you longer to graduate. Just what I have heard.
I hope this helps.