1. SAE 1045 is a medium carbon steel (carbon content 0.45%) and it's not easy to weld. Only a qualified welder should do the job.
The right electrode or wire should be chosen. Maintain the temperature as long as the welding takes place. Do not allow it to cool or cracks will appear. Then, wrap it with an insulating material so it'll cool slowly.
2. It depends on the Code or Standard you're following. If you're following ASME VIII, for example, yes, you need to stress relief the weld.
3. Again, if you're following ASME VIII, yes, A 36 needs to be stress relieved because the thickness is over 3/4 inches.
Giovanni S. Crisi
Sao Paulo - Brazil