A:AnswerYes the 50mm will autofocus on your body. It sounds as though either your 35mm is faulty or your focusing point of your 3400 isn't being placed where you think it is. Prime lens can be a little tricky. I would take it to a nearby camera shop and have them test it to see if it needs repairing.
A:AnswerYes, i use this lens with my Nikon d5500 and it works well. But the equivalent of this would be 75mm as this is an FX lens and d5500 is a DX format (might be hard when you use it in small spaces due to the crop factor). Nikkor 35mm f1.8 us available as well and that is already a DX format so you might want to consider that as well :)
A:AnswerThe winner is almost always the Nikon 85mm 1.8 for any portraits indoors or out in our opinion and for under $500 bucks. WOW! That said a very similar photo can be achieved with the 50mm 1.8 using your 810 and you can be about arms length from the infant with the 50mm. If you have an assistant to work with the baby I would still shoot with the 85. Both are very affordable lenses and I recommend you pack them both in your backpack. .