If you actually do not feel ready to commit to a relationship, then no one can force you. But I do agree with your parents that the two can go hand in hand -- in fact, a supportive partner can make it that much more meaningful. i also think that it's best not to live life according to a strict schedule, because Allah often has other plans. So if the person feels right to you and you are excited about a union, don't hesitate to pursue it. However, if you don't feel it is right, then certainly go with your gut.
The goals and personal life might not necessarily clash. Its just about management. If you think your goals can be achieved in a specific time period and you won't be missing on with your personal life till otu achieve your goals, then you can focus on your goals for the time being. But what if you regret when you don't get a good rishta after your goals are achieved?
I think if you get a very very good rishta now, you should seriously consider. If the guy is supportive in your goals, there is no harm in taking your personal life ahead along with your professional life. Don't force yourself into any relationship unless you are 100% sure that the guy is supportive in your career goals.
I think stability comes with time however, if you want to get higher education then if your partner is supportive like some one said here..then it's great.
The point of second question is, are they really that important that you want to put off one important goal of life (both for natural/normal/traditional men and women) that is.......... getting married and raise a family.
Listen to your heart and try to find out what will really make you happy. But I would say if you find a very nice rishta someone you feel would keep you happy and would care for you then do consider that rishta. Having gone through so much in life my experience says that only family and love gives you stability in the long term. Career etc will give you stability but that would be for a very short time.
Give some time to yourself . It is not easy to enter in a new relationship when the previous one actually gave you pain & bad memories. Get married when you feel like you ready to be married.
You can be married and still fulfill your goals. Inshallah if you have a good spouce, you'll also have his support and encouragement, especially for higher education. If the proposal interests you, then don't let it go just like that, think about it, maybe even disscuss your plans/thoughts with the guy.
I suggest istikhara
you can pursue your goals with your partner if he is supporting. So there is no harm in considering rishta's but make sure that they know what you want in your life and how ambitious you are.