I'm almost certain that I heard they baptize only adults.
We baptize children that have reached the age of discernment and can acknowledge why they want to be baptized. It is not just an empty measure but has to be the choice of the person being baptized that they accept the atonement of Christ. There is no set number but typically starting around the age of 9-11.
Baptising of children does happen, but it is the belief which is professed which is the criterion, not the age of the believer. As long as the child is old enough to believe the Gospel, he/she can be baptised. Obviously the age will vary from child to child, and the baptism is also not an automatic “rite of passage”.
You heard wrong. I’m a Baptist and well travelled among the Baptists here and I never heard of such a thing. Nor have I ever heard anyone claim John the Baptist as the founder. There have been people in the continuum of Christian belief who have always asserted that faith must be expressed to gain formal membership to the church. This does not mean God has no dealings with the very young or the incapacitated, we believe he does. But that remains his work, not ours to presume that we control by ritual. Baptism is a testimony of a work done by God in the heart of the believer. Without that corresponding inward conversion, there is nothing of value in the outward testimony.