You are quite right to ask those questions.
If I had time and thought I could explain this in a form that did not resemble a book ;), I would do it. However, I think I would rather point to two sources that do it better than I can.
First from a Reformed Baptist perspective I recommend Samuel Waldron's book. 'A Modern Exposition of the LBCF'.
Second: Even though John Owen was a Paedo-Baptist, his works on Covenant Theology are highly recommended in most Reformed Baptist circles.
Don't remember a work, that specifically I could recommend at the moment; but perhaps it is even in the archive of the Highway?
I think it is important to note that many (not myself) who hold to the LBCF 1689, do not like the term 'Reformed Baptist', preferring to instead be known as 'Particular Baptists'.
Hope that is helpful.