There are early-purchase discounts in the sense that when a train first opens for booking there are some real bargain fares, then those disappear as other travelers buy them, and only the higher-priced tickets remain. Take a look now on the Renfe website and you may see some price variation for the day you want to travel. You should assume that the lower-cost tickets could disappear at any time. Check fares for late today or for Thursday. The highest price you see is probably the maximum you can expect for an April trip.
There is also the Tarjeta Dorada, a card that provides discounts to senior travelers. I don't remember whether the qualification age is 60 or 62. I believe you are younger than that.
I don't know what might be available for children, but the website asks for separate head counts for travelers under 4 years old and those 4 - 13.