When can I transplant stonecrop plant that is to large in the area it is located in and can it be devided in half?
Yes, dividing a Stonecrop is quite easily done.
Dig up the entire root ball and gently pull the plant apart.
Make sure you water the plant to keep soil moist until it has become established.
https://www.gardeningknowhow.com/ornamental/flowers/stonecrop/stonecrop-plant.htm
I was given this as a gift and it's lasted through very hot weather with little water, and also through snow and ice. It doesn't seem to mind being watered a lot either? I want to get some more of it but I don't know what it is? Please help!
That is Sedum spathulifolium, or Colorado Stone Crop.
Here are some articles to help you to care for Sedum:
https://www.gardeningknowhow.com/ornamental/cacti-succulents/sedum/sedums-plants.htm
https://www.gardeningknowhow.com/ornamental/cacti-succulents/sedum/sedum-plant-pruning.htm