There are several layers to this question. I share your parents’ concerns about a relationship with someone so much older when you are so young. It would be a different story if you were a fully developed adult of, say, 40 and he 63. At that point, you would both be bringing an adult history and adult development to the relationship. The same age difference has different implications when one of the partners is just on the edge of adulthood. I always wonder what it says about an older person when they prefer to be with someone so inexperienced over someone who is a peer. However delightful and lovely you are, you aren’t at the same level of maturity and you don’t have a shared sense of history or culture. The fact that you are dependent on your parents and sneaking around to text him or see him only confirms your immaturity. The fact that he supports you in the duplicity makes me wonder about his character.
As for the threatening phone calls, I think you and the manfriend (somehow I can’t call him a “boy” friend) need to have a sit down – together – with your parents to have an honest conversation. If you are old enough to be embarking on this relationship, you should also be old enough to be open about it and to have a reasonable discussion instead of an argument. If you and your manfriend are serious,the two of you need to consider whether he is willing and able to support you instead of your parents. It is unreasonable and unfair for you to expect to live like a child with your parents providing a car and phone and a college education while you do something that is so contrary to their value system. Once you are adult and honest about your relationship, there is no risk of “exposure” because there is nothing to expose.
You can then ask your folks straight out if they are the source of the calls. If your parents deny that they made the calls, either they are telling the truth (in which case you have another problem) or they are not owning up to something they may have done in desperation to get you two apart. Either way, it will do no good to get into an argument. The two of you could then simply and calmly inform your folks that you will be contacting the police to see what can be done to stop the threats. You could ask for their support while you resolve what has become a frightening situation.
I’m sorry this all won’t be easy. But being mature means dealing with things even when they aren’t easy. How you and your manfriend handle this situation is going to tell you a lot about him, yourself, and your relationship with each other.
I wish you well.