Ensure that the tank is humid, pour some water (Don't spray as it is ineffective and won't last very long) onto your coco fibre substrate so that it is damp but not soaking and that should give you sufficient humidity for a couple of weeks.
After you have checked that the humidity is fine, leave her totally alone for 7-10 days. Do not attempt to feed her or interact with her or the babies in any way shape or form.
The birthing process can take anywhere between a few hours to a few days, it just depends on the conditions and how many babies there are to give birth to. My finished giving birth after 2 and a half days. She gave birth to 15.
Yes, take the cricket out if you can get to it without stressing the mother too much.
After a week or two, the babies will molt and will look like scorpions rather than white blobs, at this stage you have three options:
1) Leave them in to live with the mother for as long as you like
2) Separate from the mother and put them all together in a communal group
3) Separate from the mother and then keep them in individual containers.
Any of those options works fine (The second option has always been my favourite).
For the second option, they will help protect each other when one is molting acting as bouncers
However, you should tr and ensure that you put enough food in the tank for everyone in there i.e. make sure they all eat.
I left mine with the mother for approx. 17 days before separating from the mother and keeping all the babies in a larger tank as a communal group.
The behaviour I observed was amazing! I was lucky enough that they burrowed right along the side of the glass so I could always see what they were doing.