Let me start by saying that cement board is the biggest piece of .... invented by the construction industry. I do not know when this cracked but it developed by repeated manipulations of the biggest board
I would add a piece of framing behind where it is cracked. I would also make sure that the waterproofing - whatever you are doing, is done very well in that area.
Other than that you should be fine.
I want to make a few comments here:
Hardiebacker is better than the other types of cement board in general for a tub/shower wall. It is more rigid. The flex from some of the other brands is actually perfect for floors but not walls.
You should predrill your holes for cement board. Actually a double predrill. You just need a very small bit for the screws and a larger bit to pop 1/8" down to sit the heads. Without predrilling the screws often catch and create space behind the board... which causes cracking.
Why is there a huge gap in your corner? This does not look right at all. If you need to move that piece over, yes I would just replace it.
Perhaps you takes some other pictures and we can help more. Dealing with concrete board is not hard once you get the steps right. If you don't predrill, use wrong screws, have wrong type of drill, framing not flat... it can be frustrating.
Should I replace the board in the picture or screw it in place as is?
Assuming that you have properly supported the cement board from behind with studs, and you attach it, this should not present any problems.
So as long as the surface is relatively flat and is secure (i.e. doesn't move) it will be fine.