Sounds OK to me. Donīt worry about him/her eating just yet. Let it settle in for a few days before you feed it and just make sure it gets fresh water.
Try to feed it smaller crickets. If the crickets are too big they can manage to kill the cricket but will have difficulties with swallowing them.
It really doesnīt matter how you provide the calcium as long as the gecko eats it. If they eat from a calcium dish itīs fine. Personally I dust all the crickets I give to my geckos but some also have an extra dish inside their vivarium(eg Lepidodactylus lugubris which lay A LOT of eggs).
Better safe than sorry, right?
The licking of the face is most likely a comfort behaviour, so donīt worry, its normal.
Judging from the pictures you have taken the size of the gecko indicates that itīs full grown. If that is the case you should be able to see if it has hemipenile bulges by the base of the tail. If that in turn is the case you have a male. If it hasnīt, it s a female

Perhaps you can get a close-up of the tail base?
The age is not possible to say, only if itīs a juvenile or a fullgrown animal.
Iīm also posting the promised picture of my setup. Itīs rather new so the plants havenīt had much time to grow to the intended size, but I think you get the idea...
