Welcome to the Forum. I will try to help. Once a condom breaks during intercourse, the act is considered "unprotected" and therefore the person is at risk for STDs, including HIV. You should get tested. The prevalence of both STDs an HIV in many African nations is higher than in other parts of the world. Because of your exposure, if it is less than 72 hours since your exposure, you are a good candidate to receive what is called "post-exposure prophylaxis" (PEP) for HIV. There is a risk which while not higher than 1 in 1000 is high enough to warrant evaluation and possibly receipt of PEP. If you are in this time window, I would seek evaluation sooner than later. At that time you should also be tested for other STDs.
As far as your risk related to condom breakage is concerned while variables such as duration of exposure, etc are of theoretical concern, there are no studies to help us know how things change over time or in different situations. Best to just say unprotected and act accordingly.
As for your specific questions
1. See above. There is some risk. Risk for other STDs (gonorrhea, chlamydia, etc) is higher than for HIV but HIV is the tough one to treat.
2. There is no reason to think that the nicks at the base of your penis make you any more (or less) susceptible to infection than others.
3. No, there are no data to suggest that putting on another condom without washing your penis, etc was a poor choice.
Hope these comments help. Please feel free to ask a follow-up question or two if anything I have said is unclear. EWH
Thank you doctor Hook. When you say "HIV is the tough one to treat" do you mean that it is harder to diagnose within the 72 hour time frame or that if one was infected it is harder to treat or both?
The latter. If you were to get HIV, it would require taking medications continuously as opposed to other STDs which can typically be handled with a single course of treatment. If the folks you talk to decide it is appropriate, they would not be able to diagnose HIV but would be giving you therapy designed to prevent you from getting it while the infection is still incubating and is otherwise undetectable. EWH