Yes, you can get insurance for a vehicle not owned by you — the best option would be to have your friend add your name to the registration before getting insurance or get your own policy but have your friend listed there as insurable interest. You can also get non-owners insurance, but you should only opt for this if you don't plan on driving the car regularly as it only provides liability coverage, so you won't get full coverage with collision and comprehensive.
Car Insurance Costs
You are correct in that having a poor credit history will raise your rates. Age can be a factor as well.
The answer would depend on where you live or park your vehicle the majority of the time. If you live with your boyfriend, you should be able to be added to his policy.
A credit score is a section of the overall "insurance score" that partially determines your insurance premium. The reason credit is used to determine rates in most states is due to the correlation between a driver's score and their likelihood to file a claim.
I couldn't tell you with any certainty whether or not that is the case since I don't work for that company, but it's certainly possible since each company has their own set of underwriting requirements. Either way, I can imagine that you aren't satisfied by their response, and with good reason.