Hi CP.
When I first started out and before I got some good hands-on guidance, I really struggled with forge welding in my propane forge. Turned out I simply wasn't getting the steel hot enough. As soon as an experienced smith had showed me the lemon yellow I should have been aiming for, I cranked up the forge, blocked the doors and did it first time. No problems after that so persevere and you'll get it.
Re axe steel, it depends what you'll be using it for - woodsplitting, camping, etc. I would suggest you let the tool's use direct what steel to use - what proerties do you want/need? For outdoor use you may want to try something corrosion resistant like 420 stainless, but this will come at the cost of edge retention. For general purpose camp axe, I'd probably go with 1060 - but I'm sure others will have their own views.